Put your stopper in the sink. Then, using hot water, add just as much water as you need to get your dishcloth wet. Put your least soiled dishes in the sink. Then, put some soap on your dishcloth, and start washing dishes. Add soap to the cloth as needed. I put the dishes in the other sink while I'm doing this. When all of these dishes are washed, take them one at a time and rinse them off over the first basin w/hot water. This will keep your water hot and will gradually fill the sink. Stick more dishes in the sink, and repeat the process.
I've found that by the time I have a full sink of water, I'm out of dishes that need to be washed as well as room to put them.