"saam" means "together", so you use "saam met" when you do something together with someone or if you things are physically together. Some examples:
Ons kyk saam TV
- We're watching TV together
Wil jy saam kom/gaan?
- Would you like to come/go along?
Moenie die pienk hemp saam met die wit sokkies was nie
- Don't wash the pink shirt (together) with the white socks
"met" on its own is mostly use like "with" in English. It usually indicates that something is done with something else, or in aid of something, for example:
Ek slaan die spyker met die hammer
- i hit the nail with the hammer
Ek werk met wilde diere
- I work with wild animals
Help my asseblief met my wiskunde
- Please help me with my maths
Koffie met melk en suiker
- Coffee with milk and sugar
One odd one out is this:
Trou met my!
- Marry me!
I hope this helps!