Can you explain this pun to me please?
My English teacher was getting started on teaching us Julius Caesar. He told us that Shakespeare had lots of puns to start a play. So he gave an example:
"A mushroom was traveling and came to this restaurant. He saw this pretty girl and went up to her to dance. She said: Eww, but you're a mushroom. He said: Come and dance with me, I'm a fun guy."
Half of the class starting laughing. Then the othe half of the class got it after. I'm the only one who kinda gets it, but not entirely.
Can someone explain it to me please?
Ok, I'm getting lots of fungus answers... still don't get it! 
The two key words/phrases are "mushroom" and "fun guy." Say "fun guy" out loud, and it sounds the same as fungi.
Mushrooms are fungi.
So, the mushroom said "I'm a fun guy." If you hear it, it sounds both like he's saying "I'm a fungi" (which is true) and "I'm a fun guy". Puns are usually done with words that sound the same or have similar meanings.
Here's a harder pun to understand (from Shakespeare's Romeo & Juliet):
I translated what they said into parentheses to make it easier to understand.
SAMPSON
'Tis all one, I will show myself a tyrant: when I
have fought with the men, I will be cruel with the
maids, and cut off their heads.
(It's all the same. I will be cruel, after I kill the men, I will be equally heartless to the women; I'll cut off their heads)
GREGORY
The heads of the maids?
(Their heads?)
SAMPSON
Ay, the heads of the maids, or their maidenheads;
take it in what sense thou wilt.
(Yes, the heads of the maids, or their maidenheads, whatever you want to think.)
Maidenhead means virginity, so Sampson is saying, yes, I'll take their heads, or take their virginity (maidenhead) whatever you want to think. This means that Gregory can interpret what he said however he wants: either as Sampson killing the women or raping the women.
Shakespeare actually makes a lot of sexual jokes in his plays, so if something sounds dirty or sexual, it probably is.
Cinna, the Poet
