Sorry for bad formatting, but spoilers on MD don't support quotes it seems
Between or at ages 3 and 4, your child should be able to:
Say his or her name and age
Speak 250 to 500 words
Answer simple questions
Speak in sentences of five to six words, and speak in complete sentences by age 4
Speak clearly, although he may not be fully comprehensible until age 4
Tell parts of stories
...
Mind you, to speak a language fluently without having to ask "what does X mean?" every 5th sentence or so, you need to know about 2000 words.
Cognitive Milestones:
Correctly name familiar colors
Understand the idea of same and different, start comparing sizes
Pretend and fantasize more creatively
Follow three-part commands
Remember parts of a story
Understand time better (for example, morning, afternoon, night)
Count, and understand the concept of counting
Sort objects by shape and color
Complete age-appropriate puzzles
Recognize and identify common objects and pictures
Movement:
Walk up and down stairs, alternating feet -- one foot per step
Kick, throw, and catch a ball
Climb well
Run more confidently and ride a tricycle
Hop and stand on one foot for up to five seconds
Walk forward and backward easily
Bend over without falling
Help put on and remove clothing
...
Wait, I can't catch balls still, wtf is wrong with me
Hand and Finger Skills:
More easily handle small objects and turn a page in a book
Use age-appropriate scissors
Copy circles (but not squares until 4)
Draw a person with two to four body parts
Write some capital letters
Build a tower with four or more blocks
Dress and undress without your help
Screw and unscrew jar lids
Turn rotating handles
Social:
Imitate parents and friends
Show affection for familiar family and friends
Understands the idea of "mine" and "his/hers"
Show a wide range of emotions, such as being sad, angry, happy, or bored