Generally speaking the beginning doesn't really matter all that much so just start building up numbers however you see fit (some people go left right left right multiple times before crunching downwards). But start building and pinning your largest number on either the left or right corner. So, for example, try to make a 32, and pin it in the bottom right. Then start working on a 16 to its left, and an 8 to the 16's left, and a 4 to the 8's left. Generally, I try to make sure the entire workspace row is locked as often as possible by making sure it's always filled. This minimizes the chance that you'll need to unpin the largest number from its corner.
Once you've got your workspace row locked, there are a few things you can do. I haven't decided which I really prefer yet, but I basically just start creating another workspace row above the first workspace row. I'll usually try to focus on creating row #2's largest number on the opposite side of row #1's pinned corner number so that I can start crunching downwards as numbers begin to vertically match.
That's the very general gist of it. There are a few minor special case tactics you can use, but I'll leave that for you. Oh, and as faet said, don't swipe up (if your workspace is at the bottom). It's a recoverable mistake, but can make things much more difficult if you get a 2 stuck below your workspace (but it does kind of add some more spark to the game trying to recover from it). Personally, once you start using this strategy, the biggest thing you need to look out for is to not create a scenario where the game will generate 3 locked rows, because that will force you to swipe up. You'll see what I mean. Good luck.