There are 2 ways to get your slicing skill up.
First one, and the most profitable one, is going to gather the lockboxes in person.
Giving or taking 5-10 skills, you can raise Slicing by gathering lockboxes on the following planets:
|Roughly Skill LvL
|1-75||Coruscant [R] / Dormund Kass [E]|
|75-140||Taris [R] / Balmorra [E]|
||Quesh / Hoth
||Belsavis / Voss
||Corellia / Ilum
(If you somehow get stuck, or want to leave on another planet, sending a companion to make a mission for 1 skill or 2, might be a good idea)
For who’s interested, I’ve made a map with the Slicing nods in Ilum.
Please note that these may not be the only slicing nodes in Ilum, it’s all what I have found by doing dailies and farming boxes there. Either way, this should show an idea about where the nodes are spawning.
The second way to level Slicing is by sending your companions in missions. Here is the list with all the missions available and the Crew Skill level required to make them.
The missions are divided in 6 categories:
Prosperous > Wealthy > Rich > Bountiful > Abundant > Moderate (Prosperous will give you the highest reward, while the Moderate the lowest – most of the missions are Rich > Abundant > Moderate though).
If you chose to level Slicing by sending companions in missions, I recommend doing the Lockboxes ones in order to get some credits back (and even make a slightly profit).
A tip: For example, if you have a class lvl 5 moderated Lockbox mission, and a rich class lvl 4 one, the rich one will give you a better profit than the moderated one.
To conclude, there's no doubt that the most profitable way to level slicing is by gathering the boxes yourself (100% profit), but the fastest way to do it is by completing missions with your companions.