In general, most figures behind on the left foot --- but there are always exceptions. Modern English Country Dancers (ECD) always start on the right; I've heard it claimed that this is due to the influence of the post-period Minuet. It is certainly rare that any pre-1600 dance which specifies the starting foot calls for a right-footed start.
References to ``country dances'' or even ``English country dances'' appear as early as 1551 (see Cunningham's article, and Cassazza's article in The Letter of Dance, vol 2), and Queen Elizabeth (d. 1603) was repeatedly said to have encouraged and danced country dances. Unfortunately, Playford's 1651 book The English Dancing Master is the first extant published collection of ``country dances.'' There are a few earlier short manuscripts on the topic, but unfortunately neither they nor Playford give any detailed instructions as to how the steps are to be done; the introduction of the English Dancing Master has a list of abbreviations (single, double, etc.), and that's it. In fact, early Baroque dance step styling is also not recorded, and so there is a complete lack of knowledge about Country Dance steps until the middle 1700's.
The way Country Dances are done in the SCA are heavily influenced by the modern English Country Dance community. Cecil Sharp, who revived ECD early in the 20th century, used a variety of sources, including collecting descriptions of early 20th century ``traditional'' folk-dance. Their reconstruction of these steps, therefore, is not a reflection of the steps used in 1651 (or 1600), nor is it likely that there will ever be enough information to reconstruct the exact steps used for country dancing in 1600 or 1651.
Here's how the steps are done by the modern ECD community:
A single takes 2 beats, and is one step forward and a second step to bring the feet together. A double is three steps forward and a fourth step to bring the feet together.
A slipping circle, which is not mentioned in Playford but is sometimes used in modern English Country Dancing (e.g. in Sellenger's Round), is done in a circle with the dancers all facing inwards and holding hands: the dancers step sideways to the left or the right without turning their hips. Playford generally specifies doubles where modern ECD uses slipping circles.
A sashay involves a couple facing each other holding both hands, and moving sideways with a step identical to that used in a slipping circle. Playford calls this slipping (e.g. Picking Up Sticks). This step is also called ``slipping'' in the Inns of Court manuscripts.
When arming, the dancing couple grips each other's elbows with one hand, and uses two doubles to walk in a circle. Arming always appears in pairs in Playford; we adopt the convention of calling for arming left and then right, but Playford never specifies a direction.
When siding, the dancing couple advances with a double until they are next to each other with their shoulders parallel, and then use a double to return to place. There is a variant called Sharp Siding which is not commonly seen today (even at Cecil Sharp House in London); this is discussed in The Playford Ball.
The set and turn single step involves a single to one side, a single to return to place, and then a turn in place using a double. As usual, Playford gives no directional hints. The modern ECD community always starts right. I've seen it taught in the SCA always starting left, and I've also seen it taught starting left the first time and starting right the second time, when they appear in pairs.
Unlike English Country Dances, the bransles of Arbeau have very precisely specified steps. Bransles also are mentioned repeatedly in English sources of the 16th century and early 17th century, albeit without any details, and survive to the present day as traditional folkdance in France.
A bransle single left is a sideways step to the left with the left foot, and then a step with the right foot to join the left. A bransle double is two singles in the same direction. Arbeau specifies various ornaments which can be added to these steps, such as ``step, close, step, kick,'' which is specified for the Scottish bransle and the Burgundian bransle. See the discussion after the Bransles Double, Single, Gay, and Burgundian for a description of other bransle step embellishments discussed by Arbeau.
Another embellishment is the capriole, which may be done during any leap or jump and is discussed by Arbeau in the galliard section: when you leap into the air, wiggle your feet rapidly forwards and backwards in opposite directions, while keeping your legs as straight as possible. It's important to land with your knees bent in order to avoid hurting yourself.
Arbeau states that bransles can be danced as a line or circle of dances. If danced in a line, new dancers may join in the dance at the trailing end of the line. I rarely see bransles danced in this fashion in the SCA, but Arbeau mentions this repeatedly.
Many Arbeau dances do not actually require couples, although Arbeau always speaks of boy/girl couples. These dances are listed in the cheatsheets as being for ``dancers'' instead of ``couples.''
An excellent beginner article on Galliards can be found in The Letter of Dance, volume 1. One of the basic galliard steps is the Cinque Passi, which takes 6 beats and is danced to the rhythm of the first phrase of ``My country 'tis of thee:'' one, two, three, four, (pause), six-and, one... Alternately, one can follow the simple prescription of one of the Inns of Court manuscripts: ``One, two, three, foure, & fiue.''
The galliard is described in numerous late 16th century sources, with hundreds of variations on the basic step. There are also quite a few articles about galliard variations in The Letter of Dance.
Start with left foot slightly in front of the right:
kick right kick left kick right kick left (pause) jump into the air, landing with the right foot slightly in front
The last bit is called a cadence, and leaves you ready to start again, but with the left first going first. You may stand still, move slowly around the room, or turn in place using this step.
In addition to these solo galliard steps, there are also choreographed galliard dances (some for couples), and an interesting variation called `La Volta,' which is described by Arbeau. This 2-person, intimate, spinning dance was favored by Queen Elizabeth and was condemned by some in the the religious community.
The dance known as the Almain is described in Arbeau with detailed steps and improvised choreography, and in the Inns of Court manuscripts without a detailed description of the steps, but with many explicit choreographies.
In Arbeau, the Almain single and double are quite similar to the pavane single and double, except the final close turns into a step which leaves the foot in the air. A single beginning on the left is thus ``step forward left, step forward right, leaving the foot in the air,'' while a double starting on the right is ``step forward right, step forward left, step forward right, step forward left, leaving the foot in the air.'' Subsequent steps begin by stepping with the foot currently in the air.
The Inns of Court manuscripts include no detailed step descriptions, but do refer to doubles in the opening ``traveling'' section of many almains as being ``hopped.'' Arbeau specifies that you do not actually hop but merely lift your foot into the air.
I find that ending with the foot in the air is an excellent teaching tool, allowing any dancer to remain on the correct foot.
The steps used in 15th century Italian dances are considerably more complicated than the steps used in most dances in these cheat sheets. The following material follows Joy and Jealousy in content, but is highly condensed and probably has errors; I highly recommend that you look at Joy and Jealousy if you are serious about 15th century dance.
A Movimento (plural movimentii) is simply a small motion, perhaps rising on the toes.
A Mezavolta is a half turn, and usually happens at the end of another step, taking no time. For example, a doppio ending with a mezavolta takes the same amount of time as a doppio, but the dancer ends up turning 180 degrees.
A Doppio (plural doppii) in quadernaria (4/4 time) is: step, step, step, pause. The appropriate styling is to rise throughout the step, and fall back on your heels during the final pause. A doppio done in bassadanza (6/4 time) is syncopated: 1 pause 3 4 pause drop.
A Piva (plural pive) in quadernaria (4/4) is: step, step, step, pause. Unlike the similar doppio, the second step brings the moving foot behind or even with the front foot, not past it. When done in 6 it is syncopated. Note that in some instances (Gelosia, Anello), pive in quadernaria are done twice normal speed, while in other cases (Amoroso) they are done only as fast as a doppio.
A Saltarello (plural saltarelli) is: step, step, step, hop. It also has the same styling as the doppio.
A Sempio (plural sempii) in quadernaria (4/4) is: step pause. It takes half as much time as a doppio, and has similar styling. The ``step'' mentioned in several of these dances is similar; Rosina has yet to successfully explain to me what the difference is. A sempio in bassadanza time (6/4) takes 3 beats: step pause drop.
A Reverenza is significantly different from later eras. Slide your left foot back and kneel part-way, bending both knees. This step generally takes as much time as a doppio.
A Ripresa is a piva done sideways.
A Voltatonda is a 360 degree turn using a doppio step. A Volta del Gioioso uses 2 sempii to turn, and then adds a ripresa. When turning left, you should do a circle around a point to your left.
A Contrapasso (plural contrapassii) in quadernaria (4/4) takes half the time of a doppio, and is step, step, step, close, except the final step brings the moving foot behind the other foot. Contrapassii generally come in groups, and will all start on the same foot.