Let's start small.
"Un botellín por favor"
This gets you a tiny 20cc bottle of beer; The Canarian equivalent of a stubbie. These are a tradition in Gran Canaria and designed to be drunk fast before they warm up in the sun. The cost about 1.20, but bars in Las Palmas and local towns often offer five or six botellines for five euros during football games. They come in a bucket of ice.
"Una botella por favor"
Locals almost always ask what beer the bar stocks ...
"Que cerveza de botella tienen?"
Then they order Tropical whatever the answer. However, if you are offered Mahou, Estrella Galicia or Cruzcampo, give them a go as they are good Spanish beers. Feel free to order Dorada as well; It may be from Tenerife, but it's good.
"Que tienen de grifo?"
This is how you ask what draft beer a bar or restaurant has. The answer will often be Tropical, but lots of resort bars offer a range of imported beers and bars in Las Palmas offer Spanish brands on tap. If the barman says "Viva", then you've found Gran Canaria's other beer brand and should definitely try it on tap; It's made by a German brewer and is a decent beer.
"Una caña por favor"
A caña is the Gran Canaria equivalent of half a pint; A small beer that often comes in a tube-shaped glass (vaso de tubo) and should measure about 25ccs. The name comes from the fact that the vaso de tubo looks like a section of sugar cane or caña de azucar.
"Una jarra por favor"
If a caña isn't going to touch the sides, ask for a jarra and you'll get a pint of beer (more or less). A proper jarra should be 500 ml (just under a pint) but some bars serve smaller measures and still call them jarras. Most come in a mug-style glass with a handle.
"Una clara por favor"
This is how you get a shandy in Gran Canaria. Don't worry about ordering them as they are a perfectly acceptable drink on the island. You'll be asked "caña o jarra?" and "limon o Seven-Up?".
"Cerveza sin alcohol por favor"
Why you'd want to do it we have no idea, but this is how you get a bottle of alcohol-free beer in a Gran Canaria bar. "Tiene alguna cerveza artesanal?"
"Tiene alguna cerveza artesanal?"
One for the beer lover: This is how you ask if a bar has any craft beer in stock. Viva do a few bottled beers and there are several craft brewers in the Canary Islands. Let us know if you find a really good one.
How to order a Tropical beer the right way
Because the word tropical ends in an 'L', it's masculine in Spanish. You may, therefore, think that saying "un Tropical" is correct. However, the correct way to order a Tropical beer in Gran Canaria is to say "una Tropical".
Why? Because you are actually saying "una cerveza Tropical" and beer in Spanish is feminine.