Here are the most common verbs and adjectives which take the subjunctive:

insist demand important advisable
suggest propose necessary preferable
request recommend imperative
require prefer requested suggested


Present subjunctive:

I AM on time to work. It's necessary that I BE on time.
Mary LEAVES early. Her boss insists that she LEAVE early.
Joe IS happy. It's important that Joe BE happy.

Notice that all persons take BE and that the present subjunctive
of other verbs is only noticeable in the third person singular,
SHE GO, HE LEAVE, etc. Nor does the form change with the tense of the
verb:

I suggest that Thomas BE hired.
I suggested that Thomas BE hired.
I would have suggested that Thomas BE hired.

And here's the negative:

Jim recommended that we NOT TRAVEL there due to political unrest.
The postal service suggests that you NOT SEND cash in the mail.
It's important that Sally NOT GET the wrong idea.

This subjunctive is used more frequently in American English. In British
English, SHOULD is often added: "He insists that she SHOULD be there
by noon."


Past Subjunctive

It usually looks like the simple past tense, except with the verb TO BE.
Then it is always WERE in all persons. The past subjunctive is used after
these expressions when the statement is in doubt or untrue:

wish as if/though if (conditional sentences)

Notice the difference:

You act as if you didn't care. (I'm not so sure that you do.)
You act as if you don't care. (But I know you do, deep inside.)