Description: Likely needs no introduction considering the izakaya boom going on outside of Japan at the moment, but just in case: an izakaya is a gastropub, i.e. a restaurant that puts just as much effort into their drink menu. Or a bar that puts just as much effort into their food menu. There's an entire spectrum of izakaya, ranging from dirty yakitori hangouts in cramped alleys to pristine sashimi izakaya that use only the freshest ingredients from Tsukiji everyday.
System: If you order alcohol you'll pay otōshi (and sometimes even if not). Otherwise the menus will have prices for all dishes and drinks clearly displayed. Many izakaya offer nomihodai ("all-you-can-drink") options such as "120 minutes for 2000 yen," where they'll come to ask you for your last drink order after 90 minutes have elapsed.
Budget: Expect 3000-5000 yen per person depending on how much you eat and drink. Do some rough calculations to figure out if the nomihodai option is worth it for you: you'll probably find it's worth it if you order 3 or more drinks. Most izakaya will require everyone at the table to add nomihodai, since it would be too easy to game the system otherwise.
Making friends: Even if you don't have a private room/booth, the tables at izakaya often have some kind of divider making this nigh impossible. Go to an izakaya with your friends, since it's highly unlikely you'll make any new ones there.