I don't follow Gail's advice below, I don't know why you would want to get a home equity loan. I follow the advice about getting your house listed and wait until you get a ratified contract on your house. Try to talk buyers into a 60 day closing to give you time to find something you like and get it under contract. You won't need down payment money yet, you just need an earnest money deposit at this point. You will need a back to back closing where your house closes today and the new house you buy closing will be tomorrow (or the day after is better yet). Your sale proceeds become the down payment or payment in full for the new house. These are not fun or easy, but they can be done. You need to keep your eye on the market so you can jump on something quickly once you get a contract on your house.
The other way is to put a contingent contract on a house and hope yours sells before the contingency runs out on the other one. Finding sellers that will accept a contingent contract are harder and harder to find and you normally will have to pay more to get a seller to accept one. The seller will normally give you 30-90 days to remove the contingency and they will normally have a kick-out clause that says if a non-contingent buyer comes along and makes the seller an acceptable offer you will have 72 hours to remove the contingency or you lose the house to the new buyer. Any good experienced Realtor can explain all this to you, so find one to help you.