Basically, you don't train up. The level 1 of a skill is an ensign skill, the level 2 of the skill is the lt. rank of that skill.
When you open up your BO's skill tree, you'll see 3 boxes, 1 is unshaded...this is the ensign box. The middle box is your Lt. box.
So if you train your BO for something like torp spread 2; torp spread 2 will show up in that middle box. It will remain shaded until your BO becomes a LT.
Your BOs highest rank is 1 less than you. So, to promote your BO to LT, you must be a LT. Cmdr. Once you are a LT. Cmdr, open up the first tab for that BO. You'll see a button that says "promote." This will raise your BO up to the next rank, and then you'll be able to use that LT skill. Now, to get your BO to the LT rank, you just spend a certain amount of skill points on them, and they must have acquired a certain amount of merrit. The screen will tell you how much.
Finally. If we're talking space skills, you must remember one thing: Your ship must allow for a LT rank console in order to use that LT rank skill. For instance, I have two LT Engineers. On my LT Cmdr ship, a Vesper Cruiser, I have only 1 LT. Engineer console, and an Ensign level console. So, when I put both BOs onto my bridge crew, only the one in the Lt Engineer console is allowed to use his/her Lt. rank skill.