Execute triplets slowly at first. Beginning slowly helps to get the feel for the triplet pattern, and firmly provides a foundation. Building guitar triplet speed is a walk-before-you-run situation. Learn triplet patterns slowly and begin to build momentum once the patterns are ingrained in your memory. Start by playing individual open strings using the "one-trip-let, two-triplet" counting pattern.
Practice with a metronome. A metronome is a time-keeping device that allows you to set the timing speed, from largo (40 to 60 beats-per-minute) to prestissimo (around 208 beats-per-minute). Since a metronome's timing increases are graduated, you can raise the tempo when you have mastered triplet patterns at the previous one. Be sure to learn the fingering of the triplet pattern before using the metronome.
Alternate your picking. A good way to develop picking confidence and triplet speed is to alternate your picking while practicing triplets. Accomplish this by first using all down strokes with the pick, then all upstrokes. After practicing these picking patterns, switch to alternate up- and down-stroke picking.