To get started with creating Custom Fields for Contacts, click on Settings from the top menu.
Select Custom Fields from the left menu.
Scroll down to find Custom Fields for Contacts. Under the label Custom Fields for Contacts, you can add new custom fields by clicking on the blue button saying "+Add Field".
Once you click the button, a pop-up window opens up saying Add New Field. Type the field name in the text box beside Field Name and then click on Add Field.
A new custom field will show up in all your new contacts created henceforth and also can be viewed here. You can edit/delete fields from here.
To see your Custom Fields in a Contact, just go to More-> Contacts-> Create New Contact and you will be able to see an option of Custom Fields which can be seen highlighted below.
Alternatively, you can also see your Custom Fields in a Contact by clicking on the lead in your pipeline and selecting Contacts from the left menu.