Yes, I'm terrified of dentists and I just had some major work done a little while ago. Due to a small bone spur in my jaw I am very, very hard to numb (the spur blocks the main nerve so the needle can't get to it). I've been drilled on raw too many times to count. I always sit down with a new dentist and explain this up front but they rarely believe me until they try to numb me, lol.
I made sure to pick someone who would listen to me and go at my pace. I needed to know he would respond if I ask him to stop, wait, or slow down. Check Yelp and other web site reviews, that was how I chose my current dentist. It's a long drive to his office but it's very clean and relaxed with a very nice dentist. I get anxious lying on my back as you have to in dental procedure chairs. In this office I can get up and walk around whenever I need to. I usually only walk around while waiting for the numbing agent to work, but I like to know I can get up during the procedure if I need to.
I take a small stuffed animal with me to hold. It sounds silly but it definitely helps (there's another dentist office in town that keeps stuffed animals on hand and routinely offers them to kids and adults)! I also hold some kleenex in one hand in case I need to dab my eyes. Sometimes I listen to music on my phone with earbuds; most dentists don't mind this as long as you can still hear them speaking to you.
The staff there is cheerful and friendly and they don't make me feel weird for needing what I do.