Get yourself a plastic sandwich baggie, or a piece of Saran Wrap. You want it to be flat so if needed tape the corners to the table.
Next take the colors you want to use and start dotting them on the plastic. Have all your colors open and ready to go. You need to work quickly, but don't worry, you don't have to be Flash Gordon or anything, just don't let the polish dry. Use each color and try to group them in the shape of a fingernail. Make sure you get it wide and long enough for your nails. To be on the safe side make it wider than you need.
Keep alternating your colors till you have a small puddle of polish dots. Take a toothpick, dotter, anything with a point and lightly drag through your puddle. Don't mix too much or you will just have a solid icky color. If you want more of one color add more dots. You will end up with a marbled swirly spot. Make one at a time and do enough for all of your nails. Let dry completely.
Once dry you can start peeling them off and placing them on your nails. Do one nail at a time and first paint with a clear base coat. While still wet place your strip on your nail and gently smooth into place. It's going to look messy, but don't worry, we can clean it!
Let them dry on your nails for a minute or two and simply file off the excess from the tips, just like with the nail strips from the store. Clean up around your fingers with a Q-Tip in some polish remover or however you usually do this when painting your nails. Paint over with a top coat and you're good to go!
As for staying power, my home made strips are comparable to the Sally Hansen ones. You can make all sorts of designs this way and it may be easier than trying to draw on your nails. I will probably do this mainly for marbling looks.