bucking the tide
Most of the damage and injury from ukemi is from the oldest problem in the book, resistence and tension.
Believe it or not, most throws, falls, and even breakfalls have a natual rythym.
I remember the first year I started Aikido after the rough and tumble Karate classes I had just come from ... some days I thought I was going to break some of the guys because they would use way too much force to bring about the pain needed to do a technique. In the manner which I learned to do jujitsu, you brought about pain to manipulate someone, but not enough to cause damage to your partner. My Aikido counterparts were not that adept in feeling the different degrees of pressure needed for manipulation because their ukes were always pliant?
The same goes for ukemi.
You can wait to be thrown, you can try to be ahead of the throw, or you can learn to go along with the throw ... the latter being the best of all situations for ukemi.
Maybe you are stressing out because you are concerned about looking silly, or you want to be as good as the advanced students?
Don't be concerned about what others think, you will advance as quickly as you are able to ... injurys from tensing up or falling flat are not gonna help.
I am sure you have already been told to fall into a round ball from right shoulder to left hip and left shoulder to right hip while never letting your head hit the mat keeping your chin tucked into your chest or looking at your belly button when you fall?
Sometimes I wish I had videos of all the people who were falling like crash test dummys because of tensing up, or simply needing to slow down to get the natural feel of ukemi? Now, after two years, you would think these same people could never have been that clumsy, with a lack of confidence?
One of the most important things about training is to not injure yourself further if you do fall incorrectly from ukemi. Don't be afraid to modify your practice to take a throw into a stretch, or take it up to the thrown or fall? The hardest part of Aikido is getting to the throw, the throw or fall is the easy part.
I, myself, have a problem with balance that makes the room spin after ten minutes or so, so I have to modify practice just to continue. It is not uncommon, however, to shorten a technique, or modify it to your partners needs if they are injured.
I can't tell you how many times I have been with sensei's who are at seminars and they have sprains, or joints that are injured that call for modifying a technique to allow for injury? So too, you must speak up when training with others more skilled, or should I say, less skilled in adapting to injurys and ukemi that needs to be practiced and polished. Speak up. You will find almost all your partners are receptive to your needs.
As for a quick way to learn ukemi?
You might get a whole lot of tips, advice, and insight as to how to fall ... but you are gonna have to become attuned to your body taking the falls as you clean off the rough edges in practice.
Just don't be afraid to speak up for yourself and slow things down until you can take faster and faster ukemi? It will happen, in time.
Just give yourself time, pay attention, and most of all, have fun.