A good, simple homemade drain cleaner that usually works well is to combine 1/2 cup of baking soda with 1/4 cup table salt and pour into the clogged drain. Try to remove as much water from the sink as possible first so the mixture goes directly into the drain. Then pour in 1 cup of heated white vinegar. If possible close the drain with the plunger, or even duct tape, to prevent your home made drain cleaning solution from escaping, because a foaming reaction will occur.
Let it sit for about 15 minutes, then run hot water down the drain to see if it unclogs. Repeat if necessary.
You can also try to unclog your drains with lemon juice and baking soda – first pour 1/2 cup baking soda into the drain, followed by a 1/2 cup of lemon juice. Plug the drain and let it sit for an hour. Then pour in hot water. Lemon’s smell better, so you might want to try this one first, although lemon juice costs a bit more than baking soda.