1. Don't hide it--If you are the one asking, mention that you are trying to keep costs down. Naming a goal should let your potential date know you are financially responsible. So saying, "I'm saving up for a house, but I really want to do something fun and get to know you" shouldn't be a turn-off. If you are the one accepting, also don't be afraid to speak up. Sometimes it's unclear who will be paying for the date and you don't want to say yes to dinner and suddenly be hit with a large bill. Feel free to speak up and make suggestions of your own.
2. Ditch the traditional--Inviting someone out to dinner and a movie isn't very original. Show your creative side by coming up with something different and cheaper!. Many museums have free or reduced tickets on a certain day. A walk in the park is always free, and some parks even offer free entertainment like movies or theater performances. A walk or a picnic in the park is another cheap date. Hiking is also a good activity – not only does it cost almost nothing but you are doing something with your date, so you'll automatically have things to talk about.
3. Forget about food--Or at least a fancy dinner. Try keeping the food simple and easy to focus on an activity. Check out a BYOB spot or suggest meeting for just dessert. If you want to include dinner, enjoy pizza together at a local favorite and then go to the fancy place for their fondue. Just make sure to do some research and make sure the pizza place is good. If the potential date turns you down or demands an expensive night out, you know they weren't worth draining your funds for anyway!