Contigo means "with you" for example, Quiero ir contigo.(I want to go with you) Conmigo means "with me" for example, Ella quiere ir conmigo. (She wants to go with me.) Hope I could help!

hi you can use contigo when you try to do something with other person example: yo hare esto contigo,jugare contigo. when you use conmigo it means yourself example: baila conmigo,juega conmigo

Spanish is not my specialty but basically these words just mean 'with you' (contigo) and 'with me' (conmigo). It is like 'con ti' with an extra 'go' behind it so make is sound more fluent. And made into one word. I guess..