It's a Destroy all the aliens Star Trek game. You are Kirk, captain of the Enterprise. It's like a RTS except it's 2D board-style playing, you have to manage your Dilithium / Shields / Weapons, and use long range scanners, etc. There is a help file I believe, but the short and simple is:
To view the manual in Windows Vista / 7 / 8, you need WinHlp32.exe, get it from MS here.
Scratch that, just open WinTrek.doc in the WinTrek directory.
Choose difficulty (Skill menu before starting or loading a game)
Hit File > New (or File > Open to restore previously saved game)
EDIT: Don't forget to PAUSE the game when you aren't playing, so that your time remaining won't run away on you!
Your status screen tells you the Stardate, current quadrant / sector location, Dilithium remaining, Shield power remaining, Photon torps remaining, Battle condition (Green, Yellow, Red, or Blue - Blue is in spacedock), and Aliens remaining to destroy by the given Stardate.
Messages window displays mission events
Controls Window lets you switch between: Short Range Scan, Long Range Scan, Navigation, Shields, Photon Torps, Phasers, Damage report, and Computer Console
Yes, you can get hit and get your long range scanners or phasers or shields knocked out, or worse your short range scanners (which allow you to see targets) - better hope you have your wits about you if that happens.
You don't auto-raise shields in code red, so I'd recommend putting up shields as sometimes the aliens fire first. I imagine at higher difficulties it gets worse. However, moving with shields up wastes the energy into space, so travel with them down and put them up first thing if you go code red (meaning aliens in area).
Long Range Scan window --
higher numbers mean enemies in the area (although stars make for higher numbers too, but that are more like 7 or 8, whereas enemies are in the 100s -- multiples of 100 are multiple enemies). Starbases where you can refuel / rearm are multiples of 10 usually.
EDIT: OK, it's simpler than I initially thought:
Nav Window -- you can just click the direction you want on the compass, or use the arrows. Warp moves you in the selected multiple of quadrants, impulse moves you in sector (impulse can move between quadrants, e.g., if you are in SRS at the edge, impulse over the edge moves you to next quadrant). IIRC all controls are set to use keyboard (L/R multiples of 10, U/D multples of 100, Enter to Execute) You can use Alt+W+<number> to quickly open screens. Don't forget to save.
You cannot fire through stars; move around them.
Phaser lock is automatic, you can select wide spread to target multiple enemies (keep in mind you'll need more power).
Photon torpedoes are manually targetted but the computer can help.
The computer can execute some nifty commands, e.g. ricochet allows you to slingshot around a red star using minimal dilithium to traverse enormous distances.
For more detail, read the manual