If you take Japanese 101 somewhere, it won't be too long until they teach you this phrase:

一緒に
いっしょに
together; with (someone)

It makes sense to teach this early on, because it certainly comes in handy when making friends:

一緒に行かない？
いっしょに　いかない？
Do you want to go together?
Literally: "together + not go?"

Well, if you're in a class, they'll probably have you learn a more formal version:

一緒に行きませんか？
いっしょに　いきません　か？
Do you want to go together?
Literally: "together + not go + か?"

But it also proves to be rather useful later on in your studies. For example, if you're at a party with friends, you might turn to one of them and say:

一緒に帰ろう。
いっしょに　かえろう。
Let's leave together. // Let's go home at the same time. // Let's go home together.
Literally: "together + let's go home."
Note: While "Let's go home together" sounds like the speaker and the listener live together or will be spending the night together, it is more likely that they're just going to take the same train home or something like that.

If you do get into a relationship, and things are getting serious, one of you might say:

ずっと一緒にいようね。
ずっと　いっしょに　いよう　ね。
Let's always stay together. // Let's stay together forever.
Literally: "always/forever + together + let's be + ね."

You don't necessarily need to use 一緒に when talking about "together" with a person, though.

For instance, let's say you're getting ready for an awesome day at the beach with a friend. They have a big backpack that they are stuffing things into, but you don't have a bag. You might pass him/her your wallet, phone, lip gloss, etc. and say:

これも一緒に入れてくれる？
これ　も　いっしょに　いれて　くれる？
Will you put this in there too?
Literally: "this + も + together + will you insert [=insert (and) give (me)]?"

Or maybe you and a few friends are buying food, drinks, and snacks at a convenience store before a little house party. Instead of each buying things separately, you could say:

一緒に買おうよ。
いっしょに　かおう　よ。
Let's buy them all together.
Literally: "together + let's buy + よ."

Or here's an example with food, which we all love:

味濃いからご飯と一緒に食べてね。
あじ　こい　から　ごはん　と　いっしょに　たべて　ね。
The flavor is (really) strong, so eat it with rice.
Literally: "flavor + thick + because + rice + と + together + eat + ね."

The real reason I want to bring up 一緒に, though, is that there are other meanings to the word 一緒 that I took far too long to learn.

A full dictionary entry would look like this:

一緒
いっしょ
together; at the same time; same; identical

Consider the following sentence, for example:

子供の時はお母さんと一緒の布団で寝ていた。
こども　の　とき　は　おかあさん　と　いっしょ　の　ふとん　で　ねていた。
When I was a kid, I slept on the same futon as my mom.
Literally: "child + の + time + は + mother + と + together + の + futon + で + was sleeping."
Note: We just saw this a few lessons ago, but this futon is the Japanese word for a type of thin mattress you lay out on the floor. I almost translated the sentence to "slept in the same bed."

Anyways, this 一緒の布団 （いっしょ の ふとん）means the same futon.

Here's another sentence where 一緒 means "the same:"

A:
これオレンジじゃん！みかん買ってきてって言ったのに！
これ　オレンジ　じゃん！　みかん　かって　きて　って　いった　のに！
These are oranges. I told you to buy mikan!
Literally: "this + orange + isn't it! + mikan + buy (and) + come + って + said + のに!"
Note: A mikan is a specific type of mandarin orange that is popular in Japan. Also, we saw a similar usage of のに just a few lessons ago!

B:
どっちも一緒でしょ。
どっちも　いっしょ　でしょ。
They're the same thing!
Literally: "either one + the same + でしょ."

(That's an orange on the left and a mikan on the right.)

Sometimes it's a bit difficult for me to tell if the 一緒 (に) being used means "together" or "the same."

Imagine, for example, that someone is talking about some similarities you have with an evil monster of a person. You might respond to such an insult by saying...

あんな奴と一緒にしないで！
あんな　やつ　と　いっしょに　しないで！
Don't compare me to that guy! // Don't lump me in with someone like that! // Don't put me together with someone like that!
Literally: "that sort of + guy + と + together + don't do!"

Maybe that's the 一緒 meaning "the same," or maybe it's "together." I'm pretty sure no one cares.

If all of this sounds exhausting, just remember that 一緒 can mean "together" or "the same."

And if it's followed by に, then usually it will mean "together."