1) Generally he wouldn't; his parents would find someone to give him employment. Family connections were key.
2) Free labor. Apprentices worked for you at essentially no wages; there were almost no limits on the surplus value the master could extract from the apprentice and almost no oversight. Update @jwenting points out that the relationship between master and apprentice is more complex than I've presented here. He's correct: I'm going to incorporate his answer here with full credit
a master who'd not spend time and means to train his apprentice would get no benefit from him beyond unskilled labour. And the master had the added cost of housing, feeding, and clothing the apprentice as well. They might not get paid (a lot) in cash, but they were paid in free lodging and meals, Of course the quality of those accommodations was highly variable, some masters treated apprentices pretty much like slaves, others treated them well and some apprentices would end up inheriting their master's operation upon his death. jwenting
3) Read Ken Follet's historical novels. Huge generalization, but your best bet is to apprentice with someone local and then be sent off to another master for journeyman training.
Yes, this has no sources and is therefore a bad answer. I haven't researched the guild system deeply, but my impression is that everything said about guilds is an overly broad generalization that is meaningful only as an ex post facto academic generalization for analytical purposes. Real understanding of the guilds would require research into a specific guild in a specific city at a specific time.