As with most countries, you can get fancy cocktails and brews (including a chili beer) at the more popular tourist area restaurant / bars. Look for specials and happy hours for some good savings! See Where to Grab a Drink (and a Bite) in Monteverde. But budget travel, and to better get to know a place, involves drinking like the locals do.
They drink all year, then in December when the rainy season starts to end, they decide it's time to start drinking!
The ubiquitous local brew is the local Costa Rican Imperial beer. It comes in regular (corriente), light, and silver and costs around C1,200 - 1,500 ($2 - $3) in a bar and C950 ($1.50) in the mini-mart. You can get a big bottle in the market for C1,200 - 1,500. You'll find Pilsen beer around, too, but Imperial is pretty much THE beer of Costa Rica and it's everywhere. Maybe sacrilegious in most countries, it's typical to drink it in a glass over ice. Add some limón and salt and you have it michelada style.
It seems a typical habit in Costa Rica if you are driving somewhere, that you stop at the mini-mart first to grab some beers to drink them on the road. Yes, it's legal to drink and drive in Costa Rica! (but not be drunk) Pair with that the, um, less than timid Tico driving style, and you're in for quite a ride! Coming from California where you don't even get behind the wheel if you've had a couple of drinks in the bar, this really took some getting used to for me. Another local drink you might become familiar with is Guaro, or specifically Cacique brand of guaro. Guaro is a type of clear alcohol made from sugar cane, usually around 60 proof. Cacique is the brand you'll find on every bar's shelf and in every market's liquor section. It has a red label with an Indian chief on it (cacique means chief) who has 4 feathers in his headdress. If you really want to sound like a local, you can call it "Cuatro Plumas", but Cacique will do.
If you're going to drink it straight, you can drink it like a shot of tequila with salt and lime. But to do like a local, squeeze the limon (lime but it's orange inside) into the shot, and sprinkle some salt in it too. You're ready to go. Best of luck.Chiliguaro shots are popular too. It's like a bloody mary shot made with guaro and as the name indicates, can be pretty spicy! It's the sort of drink that will taste a little different wherever you get it since everyone has their own recipe. I personally like the ones that taste more like a refreshing shot of gazpacho.
Having a chiliguaro shot is almost like a rite of passage. You must have one if you're visiting Costa Rica. You can get them for a low as 4 for 2,000C (about $1 each) in some bars. I believe that might have been the same bar that used "chiliguaro" as its WiFi password. And let's not forget their fine imports of Chilean wines. They have a lot of them and the price and quality is not bad. Commonly in boxes but now in bottles is Clos de Pirque and also the Sonta is an entirely acceptable budget wine! You can get either of these for around C3,000 ($5).
Tico style is to keep your wine (yes, even red) in the fridge. That's not normally something I would do, but it's so hot, that it's otherwise impossible to keep wine at a drinkable temperature. I have had the best time hanging out with some locals here, going to their favorite bars for zarpe ("final" drink that's more like a few drinks), eating the bar snacks (bocas), and drinking. Drinking, drinking, drinking! I have gotten the Spanish word for hangover down pat (resaca or goma) and I am finally steering clear of the Cacique. It's been a blast so far but I seriously do not even have close to the drinking skills these people have here! You wouldn't believe how crowded the late night bars are (like 4am late!) and some bars are open 24/7.
One local told me that they drink all year, then in December when the rainy season starts to end, they decide it's time to start drinking! I have also been told that I "don't even know the half of it." LOL Pura vida!