Usually there are three kinds of PDF form. Eletronic(Non-fillable), Electronic(Fillable) and scanned PDF form.
This kinds of PDF form were created by some document software such as Microsoft Word and Excel. Once published, this kind of PDF can not be edited unless you have a PDF editor. Adobe Reader can only view the PDF.
Adobe Acrobat can create eletronic form that reader can fill in using free Adobe Reader software. It can automatically recognize elements on the page that look like form fields and turn them into fillable fields. Users can also customize any particular fields as the fillable form area. >>Click to view the tutorial about using Acrobat to create fillable form.>>
Scanned PDF form
One of the most popular PDF form, people scanned the paper form with a scanner and export as PDF. The form will be shown as an image within PDF, it's hard to edit it.
Adobe Acrobat can handle those 3 kinds of PDF form mentioned above, but it is highly expensive.
To fill a fillable electronic form, all you need is a free Adobe Reader.
To fill a non fillable electronic form or scanned PDF form, there are online and offline solutions that you can choose.
Just upload your PDF files then you can get started right way. But online form filler usually has file size limitation, and they are not suitable for confidential PDF files. But they are all free and require zero installation.
Just find a PDF reader application such as Foxit Reader. When you have it installed, click Tools->Typwriter->Typewriter, then you can type directly onto the form. This way is to add a new layer over the image, then add the text box where you can type in.
Or you can convert PDF to Word then fill out the form in Word processor.