To invite a partner navigate to the Partner tab. Search for a new partner by their name or by company name. You will see either the partner you are searching for or if you searched by company you will see all the available partners at that company who are visible to you.
If you still can't find the partner you are seeking, you can invite them directly by selecting the blue "email invite" button located at the top of Partner Tab. Enter their email address and click send. If you want to skip entering all your partners emails you can simply click the "add contacts" button and select which partners receive an email from you.