What do you need in order to use them? I noticed I can't even survey a city.

You need the Alphabet technology to be able to build and use spys. Investigating a city is a passive efect though, so you will need to build your espiniage points against the leader you want to survey to be able to see inside his city. Check out the espinage advisor.

How do I build my esp points?

Even at the start of the game, you have an Espionage slider. Just increase it! (Requires you've founded a city AND have met someone else.)

CTRL-E brings up the Espionage screen, and from there, you can set your Esp ratios with each civ you know. Remember to check back here each time you meet someone new, because by default, you devote 0, and unless everyone else is also at 0, that means you won't devote any EPs to that civ.

Your Palace produces 4 EPs. There are other buildings that produce EPs, give EP % bonuses, and allow assigning Spy Specialists. These EPs are then funneled into your espionage screen (CTRL-E) the way you want it.

When you want to perform an active mission, you need to build a Spy, which requires Alphabet. You then send the spy to where you want him to perform the mission, and if you have enough EPs accumulated, tell him to do it and he tries to. He can get a 10% cost-reduction for sitting still, up to a max of 50% for 5 or more turns. Also, when he's in enemy territory, he has a chance of being caught, so don't just sit them all over the place like you could in earlier Civ games.

The Civopedia has a lot more information, most of it under the "BTS Concepts" heading.

checkout some of the EE (espionage economy) RPC's. look in the Strategy Articles. spies are a great unit to steal, sabotage, etc. lookup MadScientist & Obsolete games, great to follow