I had to sign and have a client sign a PDF contract a few weeks ago and found Adobe's EchoSign to be a pretty good freemium service.
I personally just signed a piece of printer paper, scanned it, cleaned it up (adjusted the white balance, contrast, cropped it, etc.) and used the "Sign" tool in Acrobat to put it into the signature box I'd previously created. And right as I finished this, Acrobat conveniently prompted me with the option of sending the document to a client to sign online. So I clicked the button and was taken to EchoSign, which was a cinch to set up.
Basically, you just sign in with your Adobe ID, upload the document you want to send, select (or create) the signature/date field you want the client to sign/fill, and then just enter the recipient's name and email address.
The other person gets a signature request email, and they can sign it right on their phone or on their computer. And afterwards, EchoSign notifies you that the document has been signed and emails both parties a copy of the signed contract. EchoSign also stores an online copy of the signed PDF in your account should you ever need to re-send or re-print it.
I'm not entirely sure how the recipient signs the contract, personally; I just know that my not very tech-savvy client had no problem signing it, and I got the signed notification the same day.
The free account only allows 1 user and 5 transactions per month. But if you only need to get 4-5 signatures a month, it's a good free service.