Actually, there is some stuff ladies can do as a chick to make shaving easier and have better results, but it doesn't really end up cheaper.
-A scrap of flannel cloth (not a terrycloth flannel like a rag, but like a bit of what you would make pajamas from) rubbed in circles works really well at getting rid of ingrown hairs, for some reason.
-Shave twice: once with the grain first and then once against it. This helps with razorburn.
-Exfoliate your leeeggggsss. It can be as simple as a decent scrub with a rough washcloth and hot water.
-Always use some sort of cream to help raise the hairs and moisturise your skin. almost all [bar] soaps will dry out your skin and make the hairs sort of sticky because it strips the moisture out, so they are harder to cut with the razor. If you want to save money, use all the old hair conditioner you don't put in your hair anymore since you switched to that other brand.
-And, of course, try not to shave when it's too cold. Try and get the temperature of the bathroom somewhere around "tolerable", because otherwise your razor shaves off the tops of your goosebumps, too.