Step 1. Open Skype for business And search for your contacts name in the find someone bar.
Step 2. Select the tab that says Skype directory (Will be highlighted light gray).
Step 3. Find your contact and double click to add this contact. Then press Add.
Step 4. Your contact request is now seen as pending in Skype for business for Skype.
Step 5. Reach out to your contact that is using regular Skype to have them add you. (Skype does not receive a notification that someone from business is adding you.)
Step 6. Tell your contact to search your Skype for business name (the name will be you email address example firstname.lastname@example.org) and press search Skype.
Step 7. Tell your contact to click into your Skype for business name and they should no see a request. Tell them to press accept.
(It may take a moment for the request to go through). Once the contact request goes through you can now see each other online and message or call each other.