Auto-fire is your friend
I may have said it before, but I'm going to echo this here: right click your phaser icons on the UI. If you've done this right, the icons should now have green borders. When you go to attack an enemy ship, you'll only need to press the spacebar once. Your thumb -- and your spacebar -- will thank you in the long-term.
Right-click, it's the new tooltip
This one is simple, but I find it gets asked a lot in-game. Are you a Star Trek newbie who doesn't know what a Hypo Spray does? If you right-click an item and select "info" the game will inform you to a good degree. This little tip should save you a lot of "I need help..." trips to zone chat.
Press the "V" key to see
This was a feature added not too long ago. At some point you'll encounter a mission that asks you to interact with several objects strewn throughout a space or ground map. It used to suck, but now you can press the "V" key and a handy-dandy graphic will animate and point you in the direction of your next objective. Say goodbye to aimlessly wandering a zone, looking for that last anomaly to Tricorder at furiously.
Equip! Equip! Equip!
This is easily overlooked and highly important. It's easy to remember to equip your ship with new gear, because that's your prized possession. I mean, who wouldn't take care of their massive faster-than-light spaceship?
However, your Bridge Officers can be easily neglected. Sure, they're capable of being equipped with armor, a personal shield and a weapon but did you know they can equip health items or as STO calls them, Devices? Even better, when you give them an item it's taken out of your inventory, preserving precious space for bigger and better loot.
(I shouldn't have to say this, but the same applies to your ship as well. Using devices in PvP -- should you decide to engage in it early on -- is especially wise.)
Speaking of PvP...
I didn't bother with it during the early levels, but you very easily can do so if you like. When you get the order to head to the Neutral Zone, you may find yourself a bit lost. If you hit the "M" key and check our your Galaxy Map, the Neutral Zone consists of the Eta Eridani Sector Black on the map. This is the area on the far west side of the Klingon territory -- specifically it consists of the Aldebaren and Donatu Sectors.
How to not get lost
Speaking of maps and directions, you may find yourself a bit lost at times. For instance, a mission could say to travel to Argelius IV but when you open your map and look at the system list you can't find any place listed as Argelius IV. What you can find, however, is a system named Argelius -- that's where you probably need to go.
Sometimes your system list has not a single system that sounds like the place you need to head towards. At this point, read the mission text carefully and see if there's mention of a "Sector" where your destination is located. This is easy to miss, and you may just be in the wrong portion of the galaxy. Hey, it happens to the best Captains.
Knowledge is power
Your first ten "levels" should go by quickly, and before you know it you'll hit Lieutenant 11 and earn your first promotion. This is where you get to pick your first ship (I recommend sticking to your class type ship, at least for the first time) and it's so very worth the effort. Hopefully this guide will help make that journey as smooth and enjoyable as possible.
"End Captain's Log."