Alcohol is pretty much everywhere. It's almost a shame to have none in the house, in case someone comes. It's sold freely, in any grocery store, or your neighbor may sell good moonshine. Your cousins may bring a bottle of brandy when they visit.
Often it's hard to refuse a drink - the excuse of having to drive afterwards mostly works nowadays (the latest traffic law is harsh).
The usual drinking age begins around 16, though it's not uncommon to have first encounter on a doček at 14. The mitigating circumstance is that kids usually don't have the money to get seriously drunk, or to do it often. It's also good that they learn how to handle alcohol at an early age; many find their limits and stay short of crossing them.
The time of day is irrelevant. The partying traditionally begins at dusk, or even close to midnight; there are places which close at 6 in the morning. Drinking, however, isn't limited to parties - often there's drink on the job, specially in offices. There, the frequency of drunkenness during hours seems to rise with rank - it's not uncommon that a CEO falls off his chair around noon. Or at least such stories travel far. Just like everywhere else, guys who have to entertain business partners drink more than those who have to pay their drinks. Then, there are some trades who regularly drink (or nurture the reputation), like room painters, barbers and surgeons. The postmen still carry the retirements and other payments frequently in cash (though most people are forced to open bank accounts), and they are, as bearers of good news, treated to a drink. Decades ago, it was quite common for the postman to be barely able to walk by the end of a payday.
A special category of drinking is the beer in front of the supermarket, which is an institution for itself.
Update 2014: Some cities tried to impose a ban on selling alcohol after 22:00 or 23:00, in retail only - you go to a bar and it's OK. That was under pressure from the hospitality business, and it generally didn't pass. The attempt in Novi Sad was ruled unconstitutional, the first attempt in Belgrade failed but the second went thorugh some loophole. There may be other cities. The retail inspection is local, so it's the cities or municipalities who are in charge.