A contract is sent as an 'offer'. It comes as a notification on Upwork and you click it and it shows the details of the contract as well as giving you the option to accept it or not (all would be on the Upwork page). Once you accept one - you get another notification that your contract has start (again, on Upwork) and you should be able to see it under 'my jobs - all contracs' page.
It is important to note that there are two types of contracts, fixed price and hourly - for fixed price contracts, always ensure that your client funds the milestone before you begin work and if the work is large, never submit work that is not work the money that was funded into the milestone (the amount under escrow protection).
For hourly contracts, always make sure that the client has a 'verified payment' badge and that you log the hours that you work on using the Upwork App. Try avoiding manualy adding hours as these are not protected by payment protection.
This is a summary, there are more details and you can read about them in the 'academy'
https://community.upwork.com/t5/Learning-Paths/ct-p/LearningPaths
To avoid being scammed - keep yourself updated on how to indentify common scams, here is a great start:
https://community.upwork.com/t5/Community-Blog/Top-Red-Flags-for-Scams-From-Community-Member-Wes-C/b...
