We use 'meet' for planned social situations, as in 'I always meet my friends for a drink on Fridays'. We also use 'meet' for chance meetings, as in 'Guess who I met on the bus yesterday?' 'Meet with' is only usually used for arranged meetings with a person/people in a formal or business context e.g. 'The CEO is going to meet with the shareholders tomorrow.'

When talking about people, you can always just use "meet". This can be used when you meet someone unexpectedly or you had planned to meet in advance. You can only use "meet with" for the second meaning. I personally only ever use "meet" but in business situations, "meet with" might sound better.