Quite simply, the Sun moves relative to the stars. If you could see stars during the daytime then this would be somewhat easier to measure, but as it is you need some to look at night. Choose a time (say, 9pm) after dark, and go outside and look at the stars everyday for about one or two months. Observing at the same time will keep the Sun in the same direction relatively to the Earth, but over multiple weeks you can observe changes. More specifically, over time each star will rise earlier and earlier.
On the other hand, with the exception of planets, all the constellations keep their shape and relationships to each other. The implication is that the stars are rotating relative to the Earth-Sun axis, or vice versa.
After that it gets tricky, because there isn't all that much to stop you from concluding that the Sun is fixed in space and the stars rotate about the solar system once a year. Indeed, the frame equivalence of classical mechanics treks you that this is a perfectly valid viewpoint, at the minor price that the Earth-Sun frame is no longer quite an inertial frame. Detecting this is in principle doable, but definitely not as a home experiment. A sufficiently dedicated craftsman can build, given enough time and money, a working Foucault pendulum which will demonstrate the Earth's rotation, but extending this to its motion around the Sun is definitely a huge challenge.
That said, the model doesn't make much sense in and of itself. Heliocentric models are a lot cleaner than geocentric ones in good measure because they don't require the stars to rotate around the Earth every day. A model that includes the rosin of the Earth but also has the stars rotating around the solar system is a working proposition but it's definitely a strange hybrid of a proposal, with all the philosophical disadvantages of both parents.