A mission team can be part of a local church committed to a specific ministry focus e.g. homeless outreach, schools’ work, after schools children’s’ clubs. It is certainly seen in church planting work, when a new ministry needs to be set up (check out the Church Planting Initiative website).
It can also be both for short term or long term mission (Check out GLO short term mission teams). If you are in the 18-25 bracket then Firstserve (link to Firstserve website) is a way of exploring mission options too, where you will be able to see mission teams in action.
If a team already exists in the area you are interested in, then make contact with the team leaders, as well as talking things through with your local church eldership. Check out also the option “Who should I work with?”->”Para-church Ministries” using the “What are your interests and concerns”?.