Are there schematics and/or diagrams out there to build a very basic quantum system?
I think this kind of depends on what you are looking for. You asked about building a basic quantum system which you can totally do*. Just grab a good laser, single photon detectors, beam splitters and wave plates, and some attenuating filters. If you can get the laser down to a trickle of single photons you can do some fun quantum key distribution demos, and operations on single qubits (possibly on pairs if you have the right components). Now, that's obviously no computer, but since computers are built out of qubits its a start. Also as @peterh mentioned, there is lots of simulators that you can use if you want to work with more qubits now, and example being Q# that actually can estimate the number of qubits you would need to run your algorithm on a real quantum computer.
- This is still gonna be a couple thousand dollars or more, but not nearly as much as a D-Wave :) Here is a "demo" system from an overpriced lab equipment store: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=9869
The only commercially available quantum machines are from a company called D-Wave however there is debate on exactly how "quantum" their machines are.
True quantum computers in the way most of the community looks at them are not available for physical purchase, although IBM's Q Experience allows you to use their quantum computing resources through the cloud.
In terms of trying to DIY a quantum computer we are a long way from such a goal being viable.