It depends on your problem... Which is?
I'm having quite a bit of trouble with this, I understand the process of finding the area but I'm having difficulty determining the actual area I need to solve for on the graph when there are more than 2 functions. Do I find the area enclosed by all 3+ functions or all the area enclosed by all the functions?
Usually when you graph the functions (assuming you've done it correctly), it becomes obvious what area they're talking about. So if you can give us an example, we can probably help you. Most people have difficulty setting up the integration.
First find the points where the lines cross by finding the values of x and y that satisfy any pair of equations.
Then sketching the functions you can see which of these points are the ones you are interested in.
I suppose you are interested in the bounded area on the left side where all 3 functions form the bounds. You can discard the point on the right where the pink and grey lines cross.
Considering the 3 points of intersection first integrate between the grey and blue functions from the first point to the second point to get the shaded area in the image below
Then integrate between the pink and blue lines from the second point to the third point to get the shaded area in the image below