How do I create grids for an area to start mapping?

Is there any way to create grids and start mapping by grid wise?

I presume you are talking about something like the HOT Tasking Manager.

There are various instance of the Tasking Manager, but AFAIK all require that people setting up tasks need special privileges from the system administrator.

It is relatively simple to create grids in something like QGIS and these could be used (via geojson or gpx) within some editors to show you the edges of the grid.

There’s also MapCraft:
It needs a file made in JOSM with all the slices drawn. JOSM has a nice plugin called “gridify” which can help a lot.