Note: This is written for an American who wants to travel to Europe, but it can be applied generally.
Finding accommodation is the easiest part of planning a trip, so rest easy. The most important thing is to know whether one is comfortable sharing a dorm-style room with snoring strangers or those entering the room in a drunken stupor in the middle of the night. If not, pay a little extra for something with more privacy.
Hostels
For price, convenience, and interaction with other foreigners, hostels are the tops.
Some advertise as party hostels, and others have a curfew if guests want a stiff mattress instead of a stiff sidewalk. Know what to expect; a party hostel isn’t kicking anyone out for noise or (non-violent) drunkenness. In Scandinavia, sheets usually aren’t included in the price, nor is breakfast. Whereas the farther east a hostel is, the greater chance it offers a lower price and more amenities. When booking, it’s important to read what’s included, what’s extra, and what’s prohibited.
Hostel employees are great sources of information for tours, restaurants, sights, and events, though the hostel might get a commission from recommendations. Regardless, it’s not a bad idea to ask for tips, even if it’s a random hostel passed on the street.
A handful of hostel search engines provide reviews, general information, pricing, and booking. I use Hostelbookers, but Hostelworld, Hostels, and Hostelling International are useful too. I’ve no reason to use Hostelbookers above the others except I’ve never had an issue with it, and thus, no motivation to try others. It’s possible to book directly through most hostels, but the process isn’t as uniform. It might save money on a small booking fee, though.
Couchsurfing
I’ve never done it, but couchsurfing is free and connects the surfer with a local. Staying with a stranger isn’t for everyone, but the intrepid and trusting will find it interesting, if nothing else.
AirbnB
Another method I haven’t tried, Airbnb gives a more local experience. Prices tend to be between a hostel and a hotel.
Hotels
I’m not sure. Read Nomadic Matt on hotels.
Finding accommodation is the easiest step when I plan a trip. I rarely book more than a week in advance unless I’m traveling during a peak time. Hostels do a great job of promoting themselves and making it easy to find one at a certain price or location. A good flight is hard to find, but finding a hostel is like finding the screaming toddler at church.