So, I recently saw my first provider, and she agreed to be a reference for me...but I am not sure how to add her to my list of referrals here on TER. Can anyone shed some light on this?

Thanks,

Herbangparty

She must be a TER member and have a profile as well.

Tell her to read up on how to do so in the Newbie/Self Help Manual that is linked on this page

...to others you want to see as a reference.  She can also whitelist you which is the "list of referrals" you mentioned.

I think the only way to use TER itself to connect you and a Provider in the reference / referral capacity is via Whitelisting.  If she has a Profile, she can whitelist you.  
1. You have to ask her to whitelist you.  
2. She has to know your TER handle / name.  

If she doesn't know HOW to whitelist you, the instructions are in the Self-Help Center ... someplace.

If what you got was "she agreed to be a reference for me" that's still very good but outside of TER. If you call another Provider and she asks for references,  
1. You contact your reference (Provider #1) and ask her if it's OK to give her contact info to Provider #2. That also reminds her of who you are and when she saw you and anything else to nudge her memory.
2. If she replies OK, give her contact info Provider #2.  
3. Provider #2 and Provider #1 will exchange whatever info is needed.  
4. Hopefully, you get approved

Thank you all for the information. I will contact her and ask that she add me to the whitelist.

Even though it says "BigPapasan 10:15 PM" and "impposter 10:52 PM" I swear that BPsan's post was not there when I started my reply. There are sometimes random delays that result in an earlier post not appearing right away. I can sometimes tell by the number of reads:
Original Post - 75 reads
Earlier but delayed reply - 5 reads
Later but non-delayed reply - 25 reads

Just sayin' ...

...the poster is moderated.

but there is also a whitelist FAQ.  At the bottom of any page on the site, just high and inside of the pinterest button, hit FAQ. Now you're on the general FAQ page, which you should probably read also. At the top of that page, just under the chat tab is a drop down that says FAQs. (It's also on many other pages, BTW) Select whitelist from that menu and all will be revealed. If your provider doesn't know how to whitelist, send her a link to that, it will walk her right through it.