This sounds simple enough. The wall was good enough to be painted once. It shouldn’t be all that difficult to paint it again. Let’s break down a few common cases.
I'm painting over a similar color and it's in good condition
You probably don’t need a primer. If the current wall is smooth, clean and covered with the same type of paint (both are oil-based for example), you can head straight for the paint.
I'm painting over a similar color but it's in bad condition
You need to fill holes, spackle and sand, maybe even cut a new piece of drywall in to the existing wall. Your best bet is to use a good layer of primer to ensure a smooth, consistent base layer for the colored paint. In this case, your primer will mask many of the imperfections you’re trying to fix.
The existing walls are painted with a latex-based paint and I’m going to use an oil-based paint this time
You will need to use a primer in this case. Oil-based paint will not adhere to your existing latex paint layer, so you need to create a middleman, of sorts. A thoroughly applied (2 coats is a good idea) primer will allow your new paint to bond to a new layer, which is specifically formulated to bond with your new paint.
The current paint is extremely dark/bright but my new paint is the opposite shade
Assuming the wall is in good condition and the paints are chemically the same, you have a few options here. Great primer + paints exist now, which could be ideal for your situation. But you may want to compare prices and choose whichever option suits your budget.
Covering a bright color with an opposite shade will require multiple coats of new paint. It may make more sense to cover the old color in a primer, which is less expensive than your paint. This way, you will only need 1 to 2 coats of your actual color paint. The choice really comes down to what makes you (and your budget) comfortable.