During the crew recruiting period, go to the Crew Search page to search for available crew members to add to your hiring center. Once in your hiring center you can offer a contract by opening up their profile and going to the contract tab.
You have the ability to specify the length, dollar amount and bonuses for the contracts you offer. You will get messaged with a response from the driver/crew chief within 3 hours after the signing period has begun. The response will tell you whether they like/dislike your contract offer, usually with some kind of hint as to why/why not.
It should be noted that if you send out contracts and more than the allowed limit accept your contract you will be given the first ones that signed. Also, the ability to send contracts is only available during the recruiting period.