I am attempting to learn French, but one of the difficulties I have found is not understanding my own language! I don't really understand the subjunctive/conjunctive tense and I'm not sure how often I use it.

I know that this tense is used after the keyword "that". I adapted the following example from wikipedia: "It was required that he go to the back of the line". If I am not mistaken, the conjugation for the present tense is "He goes", but using the sentence after the word "that", "go" is used instead. I used this website to have a look at the simple conjugations of the verb "to go" in English: http://www.verbix.com/cache/webverbix/20/go.shtml

Similarly, I checked out the conjugations for "to be" and the website suggests that I am, You are, He is etc become I be, You be, He be etc. It definitely sounds strange. "I hope that he be quick". Usually, anyone would say "I hope that he is quick"
Check out the excellent Wiki entry on the subjunctive mood in English.
The court demanded that the accused be present for the hearing.
If I were queen of the universe, I would outlaw all wars.
The French use the subjunctive a lot more than we do in English.

"I hope" is not a good example in English. It does not take the subjunctive.

Use the present tense of demand, suggest, insist, recommend, require, and prefer to get the hang of it.

With the verb be in the (present) subjunctive:

I demand that you be on time.
Do you recommend that we be here at 8?
Sam prefers that the children be seated at the front.

Only the third person singular (he, she, it) shows any difference with the other verbs.

I suggest that he go soon or he'll miss the bus.
Fran insists that Karen take her medicine immediately.
Olga recommends that he find a good dictionary.

The expressions It is important that, It is necessary that, and others like them take the subjunctive:

It is important that you be on time.
It is necessary that he leave at once.
It is a requirement that the students be given time to finish.

Be careful. What takes the subjunctive in one language is not necessarily what takes the subjunctive in another language, even though there is some overlap.

You will rarely need the past subjunctive of French. Master the present subjunctive first.

Dude, dont forget the classic:
wish you were here

it sounds as strange, it is subjunctive, that's grammar.
oops, I was so taken by the citation i forgot to finish my post:

by the same token, you'd say
I wish I were there.
If I were the teacher...