'Join' is usually used for groups, such as 'join the club', 'join us at the swimming pool'. If there are a number of people inviting less people to do the same thing as them.
'Join in' is used to encourage people, such as 'have a go and join in', or 'just join in whenever you like'.
'Take part in' is a little more formal. 'You can take part in a focus group' or 'take part in your local council meeting'. It means to have a role in, like 'taking part in a play' means being on-stage.
'Participate in' is formal again. 'Participate in our survey and win £100' or 'If you participate in our contest, you could be the next big thing'. It's often used in adverts or by companies as a polite way of saying 'do this thing'.
'Attend' is a verb meaning 'to go to', as in 'I attended my lesson' or 'I attended the meeting'. It just means that you were present.
'Partake in' is a little bit old-fashioned but means basically the same as 'take part in'.
'Go in for' is an American term. I think it is mostly used to indicate a preference, such as 'I don't go in for sandwiches', or talking about sports you play; 'I go in for football'.