iCloud Import Contacts
If you sync your contacts with iCloud, you can import contacts using the VCard format. This must be done using the Contacts app on iCloud.com
Outlook.com Import Contacts
Other options are the online email clients like Outlook.com, GMail, Yahoo, etc. For example, using Outlook.com, you can import a CSV file of your contacts as shown below. You can access the function by clicking on "Manage Contacts" or the icon that looks like "a person with a gear" in the upper right hand corner of the web app.
Desktop Options and Manual Entry
Getting your contacts into vCard (for iCloud) may be more difficult than just inputting them manually. There are are some Excel plugins that allow you to batch convert CSV/Excel to vCard. I’d avoid the “free online converters” because you’re basically filling their databases with known good email addresses that will get most likely get spammed.
If you have access to the desktop clients, you can import into those apps and then sync with the cloud versions (I have this scenario set up personally)
The App versions of Contacts don't allow you to import, however, the desktop version of email clients (i.e. Outlook) and online services (i.e. Outlook.com, Gmail, etc) as well as Apple's own Mac version of Contacts allows you to import from various formats.