Congratulations on riding a horse. It's one of the most exciting and fun things you can do to relax and enjoy.
To answer your question about making the horse feel more comfortable when you ride, you have to be comfortable yourself.
All animals have the ability to sense how you feel when they come close to you, so if your up-tight, concerned, upset, nervous, stressed out, happy, in a funny mood, etc, they will pickup on it. And they react in a similar manner.
It's understandable that you will be a little nervous, but just try to relax and "go with the flow". Most horses who have been trained and are comfortable with people will not intentionally want to hurt anyone. If you feel uncomfortable or unsafe around a particular horse, don't get on him. Just give him a pat on the neck and move away. Find one that you feel more connected too.
Most horses are willing partners on a ride. If you have to fight with a horse to try to enjoy the experience, then you have the wrong horse.
Like anything else in life, it takes time and patience to build a relationship and it's the little steps along the way that make the biggest strides.
So, the next time you ride, first put a smile on your face and in your heart, relax and enjoy what the horse has to offer. He will feel it too.