Acrobat provides the tools you need.
To begin with, you would scan it (if the scanner supports PDF, great, otherwise it does not matter that much). Load the scanned document into Acrobat; if it is not yet a PDF, Acrobat will convert it.
Now it depends on how frequently you are going to use this form.
If it is only one time, you might use the Typewriter Tool to type in your values, and that's it.
If you intend to use that form mulitple times, you would create a fillable form. In Acrobat X and 9, you start the Form Edit mode, where you can either have Acrobat finding fields, or start adding fields manually (the second way is normally more efficient, as the first way requires often a lot of corrective work. The result is a fillable form.
Hope this can help.