1. Open the titlepack where you're going to be playing.
2. Go to "Profile".
3. Go to "Advanced".
4. Enable "Save automatically all replays"
Optionally you can also enable "Save each round separately".
These settings are on a per-title basis.
After playing online for some maps...
In your
ManiaPlanet\Replays\Autosaves\ folder you will see that you have replays with filenames like:
AutoSave_2016-01-09-16-08-08_Sirius.Replay.Gbx
These are the replays that contain all cars that drove that map or round on the map.
Also in the same folder are replays with filenames like:
eyebo_Canyon_$s$fff a simple road map.Replay.Gbx
basically it's
login_TitleName_MapName.Replay.Gbx
These are your PB (Personal Best) replays for any given map. These can usually be uploaded to MX.
To easily find a replay that was recently saved, sort the folder by "last modified".