How To Learn
I suppose that the best way to learn would be lessons with a native speaker, but I'm going to assume for the purpose of this that you're as busy/cheap as I am and looking to self-teach.
Unfortunately resources for learning Finnish are limited compared to more widely-spoken languages. For instance, you won't find a Roaetta Stone course (I've no idea whether it would be any good if there was, having never tried one). That said, there are still useful materials you should look out for.
My starting point was a book called 'Finnish For Foreigners' by Maija-Hellikki Aaltio. It's out of print now, I think, but you may be able to find second hand copies online. It might be a little dated now but I found the lessons quite helpful and the explanations of grammar clear. There is an exercise book to accompany it, and if you follow that you'll be able to pick up the basics. There's also an accompanying audio CD, if you can find that too, with a few listening exercises. I like it, although it's probably better for learning reading/writing than spoken Finnish.
That concern led me to pick up 'Teach Yourself Finnish' by Terttu Leney. It's part of the ubiquitous Teach Yourself range (I'd previously used one of their book/CD sets to pick up some very elementary Dutch) and will be familiar if you've ever tried any of their other courses. It's much more focused on listening exercises than Finnish For Foreigners, although I personally found it a bit harder to pick up the grammar. I'd say the two books work well used in conjunction, though.
With any language you're going to need to find a way of learning vocabulary that suits you. Flash cards are often a good way, but for a more high-tech alternative I'd recommend a website/app called Memrise. At its core it's effectively flash cards, but with a few brilliant innovations. For one thing, it uses 'mems', which are pictures or mnemonic phrases submitted by users for particular words to help you remember them. For another, users can record the pronunciation of words to be played along with the card. Since this is all created by the userbase rather than a central authority, even for languages like Finnish there is already a very good collection of mems and recordings.
You can choose to follow pre-existing courses (again, submitted by users) or you can make your own. Personally I made a course with lessons containing all the vocabulary for each chapter of my books, as a way of memorising it alongside my study. It then uses an aparently well-researched system of revision and testing to help the words lodge in your mind and stay there.
There are also a whole range of features like points, friends and leaderboards that make it rather addictive. Even better, it's free. It has recently introduced a premium membership with some additional features, but you still get all of the above without paying.
Finally, I also like the book 'Finnish: An Essential Grammar' by Fred Karlsson. As the title suggests, it's a pretty comprehensive guide to Finnish grammar. It's most useful where you're struggling with some particularly weird Finnish rule that you've come across in the other books and want to see it properly explained. It's also a good reference for looking things up when you're trying to put your own sentences together.