Requirements? *chuckles* No, just play normally and the aliens will build bases! Seriously though, finding an alien base depends on a few factors.
1) What difficulty level you are on.
The higher the difficulty level, the more likely the aliens are to build a base earlier.
2) How successful you are at attacking (and therefore, ticking off) the aliens.
If you shoot down and visit lots of grounded UFOs, the aliens will want to make things tougher for you and they will be more likely to build a base.
3) How many months you are into the game.
The current campaign that I am on, the aliens did not build a base until May 1999 - so hold in there! If you have not seen any bases by let's say a year in, then you should start to worry.
4) How often you send your transports out on scouting missions.
The more often you have your ships flying over a suspect area, the greater the chance of detecting a hidden alien base - or activity leading to a base.
5) How often you check your Graphs in the Geoscape screen for alien activity.
This is the biggie! Check the alien activity menu in the Graphs section more often. You will probably catch where an alien base is hidden with high alien activity and low X-COM activity in an area or country.
Hyperwave decoders are also nice (if you have them yet) for determining what an alien ship is up to! Sometimes the game (actually X-COM agents) will also reveal the location of an alien base - but this is usually if you had a bad to a so-so month. So, follow these steps, and hang in there! An alien base will soon be spotted, you can nab your commander, and continue on with the game.