There are several ways to do this depending on what your objective is;
1. If you just want a push to start type deal, that is easy but you will need another switch for the power (think race car, throw a power switch and then push the button, to turn off, flip the power switch off).
2. a modern "push to start/push to stop" switch; this is a bit more complicated and requires some type of controller that interfaces with the push button so it knows what you want to do. There are a number of systems on the market which do exactly this, however I agree that if you currently have a keyed ignition it doesn't make a lot of sense to use PB system as you will have to put the key in, turn it on (powering the system), push the button, etc.
In my case, I was looking hard at some of the modern systems, but the good ones are not cheap and at the end of the day I decided that I liked the race car style as I do not have a keyed ignition system any longer. So I have a master power switch, an accessories switch and a push to start switch (I made a panel where the radio used to go).
It isn't overly difficult but requires some planning and thought; just have to figure out what you want and how it will work. The tuner guys use the push button start all the time.