How can vegetarians build muscle?

Proteins: Ingest more soybeans, nuts, rice, tofu.

Tell you a secret --: In sports nutrition, "vegetarian" athletes are given large amounts of protein supplements, soy if the athlete's adverse to taking the more available whey protein, plus plenty of other nutritional supplements. Coaches are reality-based and employ "sports nutritionists". You aren't going to get the protein that an athlete requires by munching nuts.