Senses. Look, hear, feel, or smell for evidence of a trap. See examples. Usually a Wisdom (Perception) check against the DC specified in the trap’s description will be required. (82)
Moving at a fast pace can give you disadvantage.
Proficiency with certain tools can sometimes help.
Logic. Sometimes your senses are not enough – an Intelligence (Investigation) check instead of, or in addition to, a Perception check is necessary. (81) See examples.
Lore. A lore-based Intelligence check might help in certain situations. (81) See examples.
Magic Traps. Magic traps are usually more difficult to detect than non-magic traps. Use an Intelligence (Arcana) check to detect one. See examples.
A Wisdom (Perception) check will work on some magical device traps. See examples. An an Intelligence (Investigation) check will work on most spell traps. See examples.
Using magic. Spells or magic items may help you discover hidden things.
Passive Detection. Even if not actively searching, you might detect a trap in passing. See examples.