I have difficulty booking a hotel in Havana from Feb 1 - Feb 4 in 2016.
What would be the best way to book hotels in Cuba?
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As you have apparently found, due to the fact that the trade embargo with Cuba remains, you can't book on any US websites, nor any US based websites. That means not only the obvious "US version of Foo.com", but also "any other country like the UK's version of US-based Foo.com". (Insert many major hotel booking websites here). If you try, you either can't search because it won't show Cuba, or it'll give you an error like this one on Kayak:
There are plenty of other websites out there that will let you book though, you just need to find them!
First up, you need to find the name of a likely hotel in your price bracket in the area you want. You can search for eg "5 star hotel Havana Cuba", or go on a website like TripAdvisor, or check some blogs, or check some non-US hotel companies. The least we need is a hotel name, but ideally also a selection.
Now, search for that hotel's name. If you found one you really liked, great! Try a few of the booking sites that come up, check for the lowest price (might be on the hotel's own site), and book. If not, find a general hotel booking site showing that hotel, then search there for hotels in Havana for your dates, and see all the hotels they offer
(Since the OP seems to be having a lot of trouble following these instructions, one such 5* Havana hotel you can easily find for a quick blog/advisor search is the Melia Habana in Havana, which can be booked on the Melia site or dozens of third party hotel booking sites, and has availability on the dates mentioned. I've not stayed there, so I can't recommend it either way, it's just one example you can use to follow the later steps of the approach outlined above)