If a college player (football/basketball/etc) declares for the draft early and doesn't get drafted, can he go back to school or does declaring make them ineligible to play college sports anymore?
Regarding the NFL and NBA drafts, once a college player declares for the draft, irrespective of whether he gets drafted or not, he cannot play college sports again.
The deadline for underclassmen, sophomores and juniors, to declare themselves eligible for the NFL draft is in January. Once a player declares for the draft, they forego their remaining eligibility to play college football, which means that once they declare for the draft they cannot return to play in college.
College players who have finished their four-year college eligibility are automatically eligible for selection, while the underclassmen have to declare their eligibility and give up their remaining college eligibility.
In hockey, a player's NCAA eligibility is voided the moment they accept compensation a professional team. It does not necessarily have to be contract-related.
Using the NHL as an example, NCAA players are permitted to take part in organizational activities such as an off-season development camp provided the player takes care of all associated costs with attending.
So while an NHL team will cover the airfare, lodging, meals, etc. for players drafted or signed out of junior-level hockey, college players are there on their own dime.
In baseball, a player may declare for the draft as an underclassman, decline to sign, and be drafted again his senior year. This is a process known as "redrafting." Aggressive agents like Scott Boras use the redrafting process to maximize the signing bonuses of their clients.
In 2012, Stanford pitcher Mark Appel was near top of the amateur rankings at the end of his junior year, but was not drafted early because of concerns about his "signability" if he was anything other than the number one choice. He was drafted by the Pittsburgh Pirates with the eighth overall pick but declined to sign, thereby vindicating his doubters. In 2013, he was drafted at the end of his senior year by the Houston Astros with the first overall pick, and a maximum signing bonus.