Shim - I'm starting out quite like you. I do have references from my trio days and as a church music director, but this is how I booked my first jobs:
1. I made demo CDs of about 10 songs, all less than a minute long. I put all my contact info on the label of the CD. No need to make it fancy, just make it attractive. Put it in a new CD jewel case.
2. I printed up some business cards. 2 cards per visitation plius a few extra.
3. I went from place to place and asked to speak to the Activities Director. Usually it's pretty easy to see the AD, but if she/he is not there you can either leave the material or call back. If you leave the material, make sure you call back in a day or two and speak with the AD. BTW, get the names and extensions of all the ADs and keep them on file.
4. I was not asked to do so, but I would offer to play a free 30 minute set.
5. Be flexible with your fee. Have a definite, fair amount in mind, but be realistic and accept less if you think it will lead to more bookings.
6. Be satisfied with 50% success if this is your first booking attempt. Unfortunately, many places are booked for the rest of the year by now, so if they tell you that, it could very well be the truth.
7. Do your research first. Don't go to places you know nothing about. You need to know whether you are visiting a nursing facility, a retirement community or whatever. Be sure to find out if they have musical entertainment on a regular basis, otherwise you may be wasting valuable time and resources.

A video can also be helpful, but I have yet to need one to land a job. My music speaks for itself. Dress neatly; no need for a shirt and tie, but don't show up in cut-offs and flip-flops unless you plan to be playing at the retired sailors home.