I think speed primarily comes with experience. Reviewing will nevertheless take lots of time for good reasons. Unlike when you read a manuscript (MS) for referencing in a MS of your own, you need to read everything. You also need to think about what has been referenced in detail and evaluate if omissions have been made in the referencing. You need to look at figures and tables for errors or problems, or just to suggest improvements. If you can, you also can or should comment on the language and structure of the paper. To cap off, you probably need to read the paper more than once, perhaps not in the same detail but one read is not enough. In all, this takes time. With each review this may become easier and you will be able to expedite the review.
I personally probably spend around a working day on a normal MS. Early in my career it may have taken twice the time. Some MS may take even longer. I don't think there exist any dependable short-cuts apart from being well read-up on the subject in general, and being experienced in reading and commenting on MS and reports. I am, however, convinced that the larger reductions in time occur early on since the benefits of experience comes quickly.