Press K to open your character screen. You should be on the Skills tab. Then select a name from the folks at the left -- either your CO character or one of your BO's. Then use the up and down arrows on the right to add points into a skill of your choosing.
Note, it's a good idea to look at higher tier skills to determine what low tier skill to put points into. This way you don't get halfway through the game and suddenly decide you need to respec.
Basically, skill up means you have points you could spend. What rank are you? If LtCmdr or higher than you can spend points in more than just the first column of skill. Again, make sure you're scrolling all the way down the page. The CO has lots of skills they can put points into.