This is such a loaded question that it could even be considered a trick question. A question perfectly crafted to trick the skeptic into giving a rushed answer that's easy to attack and belittle. If they answer something like "I don't believe anything" they will sound depressed and anti-social, which is precisely one of the responses the believer is hoping for. If you try to alleviate it with something like "I try to not just believe in things" they will attack with the old tired "so you do believe in something." Also an answer like "I don't know" will be taken as admitting defeat.
An experienced skeptic should be prepared for this exact question, because it comes up so often, yet surprisingly few skeptics are really prepared for it. The answer of an unsuspecting skeptic is way too easy to make into a straw man that's easy to attack.
This is an answer that I could give to that question.
Well, that's a rather philosophical question, isn't it? If you want a philosophical answer, then I would say that I believe that most of what I perceive with my senses corresponds to reality, in other words, things that really exist, independent of my thoughts. And of course I don't mean that all of my perceptions correspond to reality. However, I believe that most of them do.
In this case I am using the word "believe" in the sense of making an assumption, something that I just have to take for granted without further justification. Another thing that I just have to believe is that it's possible to discern what's part of reality and what isn't, by using my senses and rational thinking. These are about the only things that I believe in such manner, or at least I try to.
One way to attest the veracity of something with a very high degree of certainty is if it behaves in a consistent manner, and behaves in the same way for everybody and everything. Real things tend to behave extremely consistently, and do so for everybody and everything, while imaginary things don't. And by "everything" I mean, for example, measurement devices.
In other words, the only thing that I just have to trust is that my senses can perceive, for example, the readings of a measurement device correctly. Beyond that, I try to believe (ie. just outright take things for granted) as little as possible.