This answer is out of date.
With the recent nerf to Slicing, it is, at best, breakeven to run lockbox missions. Slicing can still be a money maker thanks to slicing nodes in the open world, and, accounting for crits, if you only run bountiful lockbox missions so I'm keeping this answer up, but it's hardly the best way to earn money anymore.
So far, the best results I've had have come from Slicing. Before I get into what makes Slicing so effective, I want to point out why I've had limited success with other tradeskills:
Other Gathering and Mission Skills have two key issues. Firstly, here's an upfront investment, in credits, required to do any sort of substantial gathering. This puts a floor on the price for which you can sell your goods at a profit, and that floor is actually fairly high. Furthermore, the Galactic Trade Network is atrocious. The UI is horrible for searching for specific items or for selling or purchasing decent sized quantities. What this means is that for you, the seller, your pool of available buyers has shrunk. Worse yet, because the game is so new and the economy is not yet mature, there are a ton of people simply dumping these materials on the GTN at 'below cost' - they're just trying to recoup some of their investment as they power through to the next skill tier, or dump the mats they didn't end up using while leveling Synthweaving or Armsmech or whatever.
Crafting skills are in a similar bind - while these are likely going to be the most profitable in the long run - especially with the ability to sell 'crit' crafted items with an extra augment slot - as of now, crafting requires a fairly massive upfront sink in both time and credits. Furthermore, most crafted goods are easily replacable by items from token vendors. Simply do a few warzones or flashpoints or some quests, and you'll be swimming in mods and orange gear to slot them in. Additionally, an immature economy means there isn't much demand for high level items just yet, and the market for low level stuff is flooded. Add to this the aforementioned problems with the GTN, and crafting, while it has a high potential upside, again lags behind.
Which brings us to Slicing. First off, I want to be clear here: Slicing isn't spectacular money, and it's not particularly fast money, but what it is is easy money. That is to say: Slicing is great because it doesn't require any interaction with the larger economy, is reliably profitable, and delivers it's rewards directly in the form of credits.
So, How do you make money with Slicing?
It's pretty simple really. The key is to, first off, always be running missions (obviously), and specifically, always be running missions that reward Lockboxes - especially those labelled as Rich and Bountiful. Interestingly, higher level missions are not always more profitable. For example, the bountiful missions listed as levels 41-48, His Home is his Castle and Off The Grid, will yield a smaller profit than the level 33-40 bountiful missions, Be Careful What You Read and Pointing Fingers. While they are still profitable (and thus, worth doing for the skill increase if that's of value to you), they will make you substantially less money than alternatives.
This Spreadsheet, compiled by the excellent folks in <Revenge of the Jerks> does an excellent job of laying out exactly which missions are the most profitable, both in terms of raw credits, and in terms of credits/minute.
TL;DR: Slicing provides the simplest and easiest way to make tons of credits with a minimum of fuss. While other professions will eventually be more profitable as the game matures, at this time, Slicing clearly provides the most reliable monetary benefit - and should continue to be a no-fuss, no-muss, reliably profitable option for solo players as time goes on.