It is rude to say this so please don't. It's here to practice vocabulary and structure.
Are you old?
Are we old?
Study English in London
Let's use 'Laura' as the person we will 'meet' or 'see'.
Use 'meet' for the first time.
Use 'see' for all other times.
First: I met Laura.
Second: I saw Laura.
Third: I saw Laura.
Next: I'm going to see Laura.
The first time
I met Laura in 2009.
We use the past simple and the past tense of the verb 'meet'. The reason is that it is the first meeting.
If you want to highlight the first time you 'saw' Laura (maybe because you were at a party and noticed her beautiful dress). You could use these sentences:
I saw Laura for the first time in 2009.
I first saw Laura in 2009.
I remember seeing Laura because she was wearing a beautiful dress.
'Met' is the simplest way to say that it was the first time.
The second time
It is now 2012 and this is the second time.
I met Laura again. This means it a meeting after the first
I saw Laura.
I saw Laura again.
You cannot say 'I met Laura'. This is because it is means it was your first time.
You become friends and see Laura regularly
I see Laura every Tuesday.
I meet Laura every Tuesday.
I meet-up with Laura every Tuesday.
I saw Laura last Tuesday.
I met Laura last Tuesday.
I met-up with Laura last Tuesday.
I'm going to see Laura this Tuesday.
I'm going to meet Laura this Tuesday.
I'm going to meet-up with Laura this Tuesday.
In these examples, because the you regularly see / meet Laura, both are fine. It's because 'meet' is the shortened phrasal verb 'meet-up'.
Laura moves to Japan - 1
Laura has moved to Japan. You are going to Japan to see Laura (that's the purpose of the trip).
I'm going to see Laura.
You cannot say 'I'm going to meet Laura'. It is unnatural because 'meet-up' implies a short visit.
Laura moves to Japan - 2
Laura has moved to Japan. You are going to Japan for business (that's the purpose of the trip).
I'm going to meet Laura.
I'm going to meet-up with Laura.