Each mode can be played in many different positions on the fretboard and can be played in any key. Just as there are twelve major keys, there are also twelve possible starting notes for each of the modes. Any note of the chromatic scale can be used as a starting note for any mode. This requires a knowledge of the scale degrees formula for each mode.
Don't try to memorize them all at once. Take one mode at a time and learn the formula as it relates to the sound of the mode. Learn the fingerings for the mode and experiment with it. You should also listen to your favourite recordings and try learning some solos which use each mode.
All you need to work out a mode in any key is the starting note and the formula. Here is the Dorian mode in four different keys.