When I was younger and mowing my parent's lawn (with a fairly steep hill out back), I always just went across the hill, starting at the top and working my way back and forth and moving downward with each sweep across.
At the time I was using a gas mower that wasn't self-propelled, and I didn't find it much harder than doing the flat parts of the yard - you just need to be careful that the thing doesn't tip over toward the downhill side.
The only real downside is that when you hit the bottom, you then have to drag the thing back up the hill, but it's only once for the whole job.
The important mower characteristics are that it have a nice low center of gravity (keeps it from wanting to tip over too much), and that it have a working kill switch (modern mowers all have some kind of lever or bar that you have to hold in order to make them keep running).
Also, don't cut when things are muddy or wet - you don't want to risk slipping and ending up with a foot in the blade.
If you can't hold the mower upright as you walk across the hill, then my only suggestion is to rig some kind of winch at the top of the hill, and slowly drop the down the hill, then winch it back up for the next pass.