Generally speaking, beginners should start out on Attitude mode with manual throttle and use default values. Default PIDs usually work well enough that the beginner doesn't need to worry about them.
If PIDs need tuning, the easy way is to just use OPTune or the up coming (next release) LP EasyTune.
The simplest stabilization for a quad is Rate mode. The transmitter sticks control the quad's roll rate and where ever you let go of the stick, the roll rate goes to zero and where ever it is, that is where it stays, even if it is upside down. This is called inner loop for later discussion. Full stick may mean 360 degrees per second (one flip per second) and so half stick is flipping only half that fast and center stick is flipping with zero flip speed.
The next more complicated mode of interest is Attitude mode. The transmitter sticks control the quad's attitude (bank angle). When you let go of the sticks, the bank angle goes to zero. The quad levels itself out if you just let go of the sticks. This is called outer loop because the attitude loop actually takes commands from the transmitter sticks and gives commands to the rate loop (inner loop). For instance if the sticks command the bank angle to be 45 degrees, but the current bank angle is 40 degrees, there is 5 degrees of error and it commands the inner loop to travel at say 50 degrees per second to correct the error. If the error were 10 degrees, it would tell it to use 100 degrees per second. What was just described is the P for proportional part of the PID for the outer (attitude) loop.