Ok - an ultra sound is exactly that.
The sonographer uses a hand held transducer that transmits ultra high frequency sound waves ino your abdomen. The sound waves bounce back and give a image of what is in your abdomen.
They use a electrically conductive gel on your belly to prevent any air pockets from giving a false image and to help the frequency travel easier.
In a vaginal ultrasound (or trans-vaginal as it is called) is when a transducer is inserted into the vagina and again the ultra high frequency sound waves a re emitted to provide an image of the contents of your abdomen.
The sonographer will change the frequency to give the best image - the higher the frequency the deeper the sound waves will penetrate - so if you are on the large side they will use higher freqeuncy to bump the sound waves past your excess fatty tissue.
There is no x-ray procedure involved as x-ray can be harmful to the unborn baby.
If you are in the very early stages of pregnancy it is possible to miss the embryo, which is why sonographers perfer to to the first scan around 10 - 12 weeks.
A large percentage of all pregnancies spontaneously expire within the first 8 weeks (another reason why sonographers like to wait). Not so long ago, before pregnancy tests became so accurate this would simply have been classed as a late/heavy period and no grief would have been caused.
Everything has good and bad points - the good of early accurate pregnancy testing is that you can get pre-natal care quickly, the bad is that these pregnancies that were never going to develop anyway are now seen and then the mother grieves for her unborn child.
Hope this helps.