Most clothing is unlocked by getting A Rank in the Hi-Score Derby modes. All clothing can be color customized by using the shoulder buttons (by default it's your Mii's shirt color).
Cloth - How to unlock
Basic Uniform - Get an A Rank in Bat & Switch's Hi-Score Derby A.
Business Suit - Get an A Rank in Bat & Switch's Hi-Score Derby B.
Caveman Suit - Get an A Rank in Gear Games' Hi-Score Derby A.
Football Uniform - Get an A Rank in Volley Bats's High-Score Derby B.
Kung-Fu Outfit - Get an A Rank in Cage Match's Hi-Score Derby A.
Manager's Jacket - Get an A Rank in Gear Games' Hi-Score Derby B.
Ninja Suit - Get an A or A+ Rank in Bat Master.
Pro Ump Outfit - Get an A Rank in Make the Call's High-Score Derby A.
Rusty Slugger Jacket - Purchase all 10 of Rusty's games.
Sweat Suit - Get an A Rank in Cage Match's Hi-Score Derby B.
Tropical Shirt - Get an A Rank in Volley Bats Hi-Score Derby A.