The bad news is that every room is different. The good news is that a basic introduction to the principles of acoustics should help you to solve most problems.
Sound waves prefer to travel in circles, like waves from a stone dropped into a pool. For PA purposes, this pattern is difficult to work with, so PA speaker cabinets are engineered to direct sound in more manageable ways. Essentially, they project out into the auditorium before the sound begins to disperse into its natural pattern.
It's worth trying to determine how your speakers radiate their sound, so you can place them to maximum advantage. And be careful how you place them in relation to each other - the sound from one speaker can cancel out the sound from another.
The one factor over which you have very little control is the room itself. Glass, concrete and tiles are the enemy of good sound, because they reflect sound waves all over place. Short of carrying your own supply of very thick foam rubber to fix to the walls, there's not much you can do, though you should try to place the speakers to keep the damage to a minimum.
A 'sound check' is essential, but take nothing for granted - a lot changes once people come in. The audience does at least help to reduce the reflected sound, but it's vital for everyone on stage, and the sound engineer, to take note of the way the sound has changed and adjust their settings accordingly - it's normal to experience a substantial loss of high frequencies and reverb.
Your biggest challenge will come when playing in the open air. Sound waves lose their energy rapidly, so you will need a much more powerful system to cover a relatively small space.
In larger rooms, a delay line may be required. This is a system that delivers the sound to the back of the hall. However, for listeners sitting mid-way between the front and the back, or at the sides, there is a risk that the two speaker sets will conflict, creating a noticeable echo. In a delay line, a time delay is built into the signal path, equivalent to the distance from the front speakers, to ensure that the sound is delivered consistently to all areas.
A typical line array
Larger venues need larger sound-reinforcement systems, with more square inches of cone to push the air. The trouble is, the more speakers you have, the greater the risk that some of their frequencies will cancel each other out, and you will actually end up with a worse sound than from a single speaker. 'Line arrays' are designed to combat this problem, and have become the standard for larger arenas and outdoor events. They are built using speaker modules with clearly defined beam angles - that is, the breadth of coverage of the air pushed out. By aligning these modules carefully with each other, you can actually build a single, cylinder-like column of sound in which all frequencies are transmitted without conflicting with each other. You can also distribute a full sound to a large and scattered audience of the kind you get at festivals. Unless you are a professional sound engineer, however, you are unlikely to have to concern yourself with the complexities of line arrays. By the time you're playing venues where they matter, you can leave it to the roadies to sort things out!