For a three year old, I would not suggest a formal academic schedule of studies (I assume you mean like a full or half day of kindergarten with desk and rote work.) At that age, they are still assimilating so much just by playing, imitating, conversing, observing, and being. For example, they are still developing behind-the-scenes in social norms, skills and relationships; early language (both grammar and vocabulary); as well as fine and gross motor control. Curiosity and exploration are the best learning tools at that age! That being said, I like to immerse them (as the previous poster suggested) in learning in daily life, in a VERY informal (and fun!) way. This, however, is something that we as parents have been doing since they were infants! I am sure you have been doing the same, whether or not you are aware of it
Much of it just happens all very organically. I think things progressed something like this:
1) Recognizing and naming familiar nouns (any and all persons, places, and things).
2) Identifying various animals/insects (both domestic and exotic at the zoo) and then the sounds they make (e.g. The owl says “whoo”).
3) Identifying and naming colors. First primary colors: red, blue, and yellow. Then secondary colors: purple, green, and orange. (You can also talk about/experiment with which primary colors mix to make which secondary colors). Then black, white, brown, and grey. Eventually you can advance to magenta, vermillion, aquamarine, etc., but that is not necessary at this stage
4) Identifying shapes. First simple ones (circle, square, rectangle, oval, triangle, heart, star) then you can advance to more complex shapes, if desired (crescent, semi-circle, pentagon, hexagon, octagon, trapezoid, rhombus, etc.)
5) Identifying tools and what they do (A hammer pounds, bang!)
6) Identifying and naming feelings.
7) Identifying and naming vehicles/modes of transportation.
8) Counting to ten. Then, recognizing the numerals 1-10. (Then counting to 20. Then recognizing the numerals 11-20. Progress as desired.)
9) Identifying and naming the letters of the alphabet (uppercase).
10) Identifying and naming the sounds the letters make (B says “Buh”).
11) Identifying and naming the letters of the alphabet (lowercase).
12) Identifying construction vehicles and what they do. (Excavators dig, cement mixers mix, bull dozers push, etc.)
13) Next would be rhymes, opposites, “same and different”, and scientific/mathematical concepts discovered via exploration, such as floating and sinking, and magnetic attraction with various objects.
For fine and gross motor skills, child development/milestone checklists can help you see if you are on track (e.g., a three-year can ride a tricycle and catch and throw a large ball). You can also them as a tool in evaluating the appropriate level of development and independence (e.g. from using utensils and potty-training to dressing oneself and tying one’s shoes).
I like to begin tracing at age three as well (you can buy colorful activity books with dotted lines for tracing shapes, curves, lines, etc..) These are a good step for learning pencil control, which will be necessary later when they begin to print letters and numbers, but to a three year old it is as fun as a coloring book. Cutting along lines is another skill that they will need for kindergarten, but I like to hold off a bit on that one! Pasting, coloring, and painting are also great at this age, as are working with lacing cards, threading jumbo beads, and manipulating playdoh. (All these take coordination but are a form of play.)
Faith formation can be as simple as going to church, reading bible stories, learning a few prayers. Social skills and manners are acquired more or less organically with a bit of parental guidance in social settings, such as the playground, local pool, library, play group, gym class, restaurant, church, grocery store, etc.
I hope this helps!