Every Labour party member decides for themselves how involved they want to be, and party involvement can change over time. See what level of involvement works for you, there is no obligation to do any more (or less) than you want to.
A good place to start is to come along to your local Branch Labour Party (BLP) meeting. These are usually held once a month, look out for emails from your branch secretary announcing meetings, you should receive these at least 7 days in advance of the meeting. You can expect discussions on motions and policy, speakers on topics members have expressed an interest in, reports from Labour councillors for the ward and the announcement of campaigning activities such as canvassing and days of action. After meetings, people may often socialise. Your local branch may also organise informal social events especially in the summer and at the end of the year.
Branch secretaries generally try to organise for meetings to take place in accessible venues, but please do let your local secretary know if you have specific requirements.
Also look out for emails announcing campaigning events and canvassing sessions, particularly online at events.labour.org.uk.