Most sites will offer an affiliate program, in which you simply become a marketing partner. Generally there are only terms to read and accept for these. That's the easiest way, but most of the large travel sites won't open up API's for you to connect to under those circumstances. Check HotelsComined, DoHop etc who do (or at least have in the past) offer affiliate programs that may suit your needs. I would suspect that if you have limited traffic/customers at this point, most will steer you to an affiliate program until they deem you have enough traffic or affiliate sales to warrant moving you to something like a partner status. Keep in mind, that you should consider what licenses etc you might been with the various options. I know in Australia, in order to become a 'travel agent', you need a license for such an activity (it's simply a 'process' these days, without much red tape).
You can start online traveling business using white label solution from travelpayouts.com They have all required tools: hotels booking, air tickets, search forms etc. You just have to 'compile' it into your own website with your branding and market it. I have positive experience for about 4 years working with them. Definitely recommend.