As mjax said, just make sure you get points with every move you make to up your score multiplier. As soon as you make a single move without getting points, your multiplier will reset to 1.
You should also realize that you can simply drag rows out of bigger columns to 'drop' them upwards, which can get you out of a situation where otherwise you'd have no options.
Something I didn't realize until I'd played it for a while, they don't have to be in rows or columns to count as a combination. Having them touch each other in any direction is enough, so having them like this .: counts too.
One thing you should try to do is play as much in the upper region as possible, to improve your chances to get a combo (playing lower down makes less thingies fall upwards).
Also try to make your moves affect more than 1 column at a time for the same reason.
Other than that it's mostly luck to get unexpected combos. I only played the game three times and got the current highscore of 308250, so it's got nothing to do with experience or skill