I am new to QGIS. I have a map with known coordinate points. How can I manually enter these points and then export this map as a .tfw??
First create an empty shapefile in QGIS from the menu bar: Layer > Create Layer > New Shapefile Layer. Create fields to hold the information about the points you're going to add.
Then the plugin I would recommend for adding single points (ie. not TOO many) is called NumericalDigitize.
Once installed and in an edit session you'll end up with a little button like this on the end of your editing toolbar:
...and it will allow you to add a feature by the X and Y coordinates you have:
Finally to save the map, you can create a quick export by going to Project (menu) > Save as Image and choose the TIF format.
This will save a TIF file with an associated .tifw file, which is the georeferencing information.
If you have the points in a spreadsheet, you can use the Add Delimited Text tool in QGIS.