How can I do better than chance in Uno?
You're trying to run out of cards, and the opportunities to change colors are somewhat limited. Your goal, therefore, should be to play the last card of one of your colors, then be able to switch to another color you have on the next play. This doesn't always work, of course.

When changing colors (via wild or matching the card), you should switch to the color that you have the most of. Switching to the color that you have the most cards in gives you the best chance to "even out" your hand; if you're stuck with 7 cards in your hand, it will be easier to play when you have 2 yellows, 2 reds, and 3 greens than to play when you have 5 yellows and 2 reds. Note that it will be easy to play one card when you have a four-card hand consisting of one of each color, but it will be hard to go out with such a hand: changing colors is somewhat difficult, and you can't count on it happening when you want it to.

When somebody calls "Uno," it's best to assume that their last card is the same color as the previous card they played; otherwise, the player going out is hoping against hope for a lucky play. Therefore, you change the color in play after somebody calls "Uno," by whatever means is handy. (Or inflict a Draw Two or Draw Four Wild against them.)