I recently moved from SVN to GIT and the process was (relatively) simple.
There are many GIT tutorials and after setting the GIT file (init command) and using the Git Bash (I prefer git ui) you can add pull the data from remote.
The MyEclipse “Teams” selection supports a “share” where you can select GIT. Since you already established .git by the “init” command, MyEclipse finds the .git, and you just accept the selection.
If the remote projects are MyEclipse projects (with .metadata etc.) you should be ready. If not, you need to establish a project structure and then pull data into it.
I hope this helps.