In it's purest form ます、ました、and ません are just conjugations. So a good example demonstrating the differences is to use 食べる (because it's breakfast time and I'm hungry).
食べます - I can/will eat
食べました - I ate
食べません - I don't eat
For ございます, it's a bit more tricky. ございます is used as a polite form of ある, the verb for "to exist". So an example would be if someone asked if there are eggs in the fridge.
So for the above example, ある is being used in ます form to make it polite and then ません is added in that funny Japanese way of asking if something exists by asking if it doesn't exist. For the second example, ございます is being used in place of ある to make it even more polite.
For your example of ありがとうございます, the ございます is being used slightly differently here. The proper etymology of ありがとうございます is meaning that "there is something that exists that I would like to express thanks for". So, the ございます here is referring to the "something that exists"． However, it is mainly used to just make sentences more polite.
ありがとうございます - Thank you
ありがとうございました - Thank you (for something already done)
ありがとうございません - Not used at all. If you really want to tell something that there is nothing you want to give thanks for, you could say "ありがたくはありません". If you say this in any setting outside of funny things to say with your Japanese buddies when drunk, this is most likely going to get you in very hot water very quickly, haha.
As for どうも, it is just another way of adding more emphasis to a sentence. You can use it in several instances, not just with ありがとう. So for example:
どうもありがとうございます - Thank you so very much!
どうもすみません - Please excuse me very much
You have to be careful when and how you use どうも though, because it's one of those words that can very easily be seen as sarcastic. So, for example, if I said どうもすいません (すいません is a speaking way of shortening すみません) in a condescending voice, it's likely I'd have some serious trouble on my hands.
I hope all this helps!