The free weekend actually started yesterday, so you can dive in and make with the shooting anytime you like until 10 am PT/1 pm ET on September 17. You'll need Uplay to take part, which you can download here. Any progress you make during the free period will carry over to the full game should you opt to pick it up. The freebie covers the full base game, but not any DLC content—although I can't imagine that will be an issue if you're just getting into it.
If you're suitably impressed by the experience, this is also not a bad time to spring for the full game, as long as you don't mind not having it on Steam: It's still full price there, but the standard and gold editions, and all the DLC, are on sale for up to 70 percent off on the Ubisoft Store.