I want to fund basic research, particularly one research lab which does what I like. Can someone point me to resources on how to set up a fund to support the research? The fund would be in USA, and the lab is overseas.
Talk to your attorney or certified public/chartered accountant and the development or giving department at the university in question. Both deal with these kinds of issues constantly. You need tax advice in your location and giving advice in theirs. These are common questions for universities which like to receive charitable donations and want their donators to be best advantaged in their contributions. They may be able to recommend attorneys and accountants with experience in donation laws in your and their jurisdictions.
Assuming this is a university lab that you wish to fund, you could contact the head of the lab and/or the pertinent administrative unit (e.g. VP of R&D) of the university that they belong to. Depending on the amount of money involved, the size of the university, and how well-connected you are; you may even consider contacting the president of the university.
It is likely that the university has been a party to this sort of arrangement before, or that they are at least prepared. Most probably they already have procedures, frameworks, contracts, etc. that can guide the effort. They can also advise you on legal and tax-related issues.