Star Trek

Click the Starfleet symbol near the mini-map to open your mission journal. You should see the next chronological mission (in this case, the one you accidentally dropped). If so, click "Hail" and reaccept the mission.

If you don't see that mission on the front page, click "Available missions" and find it there. Or click "episodes", then whatever front your mission is in (probably Klingon Front in this case).

Not at all! If you press "U", a menu will open up displaying your character. On the left, you will see your character's name, your ship, and all your Boffs. One or more slots at the bottom will probably be greyed out. These are free slots, which you can fill with new officers.

Officer candidates that haven't been comissioned yet will be stored in the "Stations" tab. You can have up to twenty or so stored there at a time. Just double-click on one when you want to comission him/her.

Go to "Stations". Normally, each of the ship's stations is manned by a Boff. One of them probably says "None". If so, click it and select the Boff that's not yet in use.

You have the Lieutenant Commander-level cruiser, right? One science, one tactical, two engineering?

So now that I got a new ship, should I decommission the old one?  Do I get dilithium from it?

I recommend keeping old ships if you have slots to keep them.  You might want to use them later for some reason.  Plus, they may create a fleet admiral position later.  If they do, you may be able to use your old ships.  Some of us like those lower tier ships and have been hoping the game finds a way to make them relevant again.

Try getting an Engineering boff, then.

No, you get nothing. If you decide to decomission a ship, I recommend you first remove everything on it (weapons, consoles, etc) so you can use them later.

And I concur with Matthias. Hold onto your ships unless you need to make room for more.

I am so excited! I am about to start playing STO.