You will be able to see Datacrons from quite a distance as they emit a large glow around them and shoot a beam of light into the sky. If you are very close to a Datacron you will also be able to hear the sound from them.

Datacron Locations By Planet

Ord Mantell | Tython | Alderaan | Balmorra | Belsavis | Corellia | Coruscant | Hoth | Ilum | Nar Shaddaa | Quesh | Republic Fleet | Taris | Tatooine | Voss

Tatooine – 5 Datacrons

Orange: Cunning +3

Location: 2139, -3671
In Anchorhead above the Underworld Trading Trainer you will see this Datacron. In the northwest corner is a corner with a pile of sand you can use to climb up and get on the wall (you must be outside of the main city wall to do this). Once on the wall, follow the path jumping from rooftop to rooftop and platform to platform. Eventually you will reach your Datacron!

Purple: Willpower +3

Location: 2074, -577
Start at Coordinates 2094, -466 and head South. Eventually you will have to jump down to a big ledge which goes into a cave (you can see the ledge but not the cave). Once inside the cave you have to go through some mobs and elites but at the end of the cave is your Datacron.

White: Aim +3

Location: -620, -24
WARNING for Republic players on PvP servers: This takes you though the Imperial quest side on Tatooine!

Start at Coordinates -724 , -894 and go through the cave into the Imperial questing area. From There go to coordinates -337, 92 which will take you into the Heroic Area (you may want bring a group with you for this one). Then head to coordinates -597, -57 in the Heroic Area and from here look over the ledge. You will see the Datacron. You will then have to drop down very carefully and the Datacron is all yours.

Red: Strength +3 and Blue Matrix Shard

Location: -2388, -1388
This path will get you two Datacrons in one trip. One will give you a Strength buff, the other a Blue Matrix Shard. Start at coordinates -2339, 6 on the buried Sand Crawler and wait for the Jawa Balloon. It can take some time for it to show up. Once it does, jump into the basket and ride it (about 1/2 an hour) until you see the Sand Crawler with the Datacron at coordinates -2389 , -1393. Jump from the balloon on to the Sand Crawler and claim your first Datacron for your Blue Matrix Shard. From there you drop off to the lower part of the Sand Crawler and hug the wall (make sure to have your run turned off and your walk turned on – its the / button on the number pad) so you can drop down onto the ledge right next to it and get your Strength + 3 Datacron.