Even Adobe's own software is not good at doing this or making clear how to do it.
With Adobe Acrobat X, you can create a text layer through the menus (View | Tools | Recognize Text) or by click Tools in the toolbar and then Recognize Text in the Tools pane.
You then have options to perform OCR on the document or find "suspects". The "suspects" are possible OCR results that don't look right (don't spellcheck?). Once you have gone through the suspects, there doesn't seem to be any way to access or edit the text layer again short of redoing the OCR.
You can choose page ranges to limit OCR (e.g. if you have a multilingual document), but you can't limit it to a selection.
Given that this is such a useful feature, it's disappointing that Adobe don't make it very user-friendly.
Edit: Two other possible solutions.
Adobe Acrobat using ClearScan
When you perform OCR with Adobe Acrobat you can change the PDF Output Style from the default Searchable Image format to ClearScan. This format will actually change the image as well, replacing characters with outlines derived from the OCR. This would both make your PDF more readable and add a text layer, but it does change the original image.
Infix PDF Editor
This program does seem to be able to display the text layer, but it still seems tricky fixing places where Adobe's OCR goes wrong (e.g. lone words in their own positioned para).
Sadly none of these options are freely available.
Best Answer
Not really. Handwriting recognition is a hard problem and the failure to crack this was one of the key reasons that the Apple Newton failed. Palm had to make a pseudo-script called 'Graffiti' in order to recognize it, and that was done one letter at a time on a special pad, rather than written as a script.
You could try an OCR program - it might work, but at best you will probably have to spend quite a bit of time fixing up the errors made by the program.
An alternative might be to try something like rentacoder.com and see if you can pay someone to enter the text by hand. There are quite a few people in developing countries who work through this, so it might be possible to get it done quite cheaply. Alternatively, there might also be someone who has a Mechanical Turk application that does this.