Use Words with a Lot of Different Letters: Because Dordle chooses two words at once, your starting words should contain a variety of popular letters. With many potential options, selecting words such as CRANE and SLATE will weed out a larger set of letters.
Track Clues for The Two Words: Use the colors for each different word. If you get a letter green, yellow or gray for the two different word puzzles, then that's what you include in each of them, don't mix your clues. Keep track for smarter next guesses.
Test out New letters Early: When using your first 3, just use new letters that have not already been played in either word. Use as many new letters as possible until its remaining words can be formed.
Use Character Frequency and Patterns: For instance, there are many words that are made up of the letters (E A R O T L S) and this may be of use to you. As you reveal some letters, look at the puzzle and try to determine likely word groupings so that the other puzzle can be efficiently solved at the same time.
Check for Overlaps and Double Letters: Certain words have double letters such as LL, EE or SS. Another aspect to look at is a letter that occurs in each word, but in different position. Looks like such a trivial detail but it can help you narrow down the options.