How can I import contacts using API?

Firstly, you need to know the Nurture's End-point. Its End-point is https://nurtureapi.nurturehq.com/add_website_contact.
On this End-point you have to send data with POST Request.
This End-point can accept the following data:
account_id : MTQ5 (Mandatory)
email : peter.lynch@nurturehq.com (Mandatory)
first_name : peter
last_name : lynch
name : peter lynch
title : Manager
phone : 486-589-7852
address : 3418 Maroun Place
city : San Jose
state : California
zip : 95148
country : United States
timezone : Pacific Time (US & Canada)
birthdate : 08-12-1982
department : Engineering
description : General manager
fax : 485-963-7526
mobile : 789-254-9138
lead_source : vaibhav
company : Nurture
tag : Trial|Active customer|Lead
add_tags : can be array e.g. add_tags[]=tag1&add_tags[]=tag2
The Account ID is present in your Nurture Account in Settings Tab.
Go to Settings Tab by clicking on the gear icon located on the top right corner. On the left pane you will see "Setup Tracking Code". Click on it. You will be moved to the detailed page of the Setup Tracking Code. Now in that a embed script is given. if you observe that script, you will see the n="sometime", this something is your Account ID.
For example: The script of your account is <script type="text/javascript" src="//nurtureapi.nurturehq.com/assets/javascripts/ntracker.js?n=MzE4"></script>
from the script the part which is bold format is your Account ID i.e. MzE4.