The best strategy to remove dots, especially as you you progress through harder levels, is to make squares. Making a square with four or more dots of one color will remove all the dots of that color from the board. This is often the best way to get a high score! Squaring isn't a catchall for winning every level, but it is the most effective way to remove a large number of dots at once.
Two Dots has an optional feature where the game will flash a potential square when one exists on the board. If you would like to turn this feature off you may do so in the in-game Settings menu.