Do you mean transfer one contact or all of them?
If you just want to move one contact, go to your contacts open one. And, at the bottom of the contact tap Share Contact, then use Message or Mail to send it to yourself. When the contact arrives on your other device open it, go to the bottom, and tap Create New Contact.
If you want to transfer all your contacts you can use iCloud to sync contacts across both devices. Open Settings->iCloud. Make sure you are logged in with your Apple ID then turn on Contacts. Do the same for both devices.
You can also sync your contacts with your Mac computer using iTunes. Open iTunes plug in your iPhone and select the iPhone, then click on the Info tab and turn on Sync Contacts and, click the Sync button in lower right. Then do the same with your iPad.