I am really upset with star trek online! Here is my predicament. When ..

Certainly. First off, what type of ship do you use? What rank are you?

Dilithium crystals can be obtained quickly by selling C-points or by doing STF's (level 45 and up)

Go to The Beta Ursae sector block, open up your map and plot a course for the Dilithium mine.
Talk to the alien, she will give you two options, click the one that is not a mining claim (Unless you do have one then click the mining claim one) and get a suit to use, turn it on and exit the airlock, you then walk up to some dilithium rocks & crystals it it will say 'mine rocks', click that and match the red outline with the shape.

Some of your question have been answered but I gotta add. You need dilithium Then the best way to gain dilithium is to do the daily mission's that provide dilithium as a reward. You can also mine dilithium at the Vlugta dilithium mine holding. Plus if you join a fleet you can also do dilithium mining at the fleet dilithium mine. PvE's and PvP's can help and you could also buy it from the dilithium exchange but that requires Zen. I noticed you have trouble with gaining Energy Credit's. The is the simplest thing to get now since all you have to do is queue up for a special farming mission in the Foundry. The mission is called "Admiral Bobo Goes To War!" (I only know the Federation varient tho) This will give you loads of drop's which you can then later sell and gain Huge Amounts of Energy Credits. The mission is quite funny and very easy. All you have to do is fire on enemy ship's without moving you ship. A few time at level 50 I was able to gain 1.3 million energy credits from just one mission.