Yup, most medical personnel seem to be fascinated by that when they find out, and to tell ya the truth a standard embalming isn't that interesting (the complex ones can be) and the public interest really stems from how guarded from the public embalming is.
A typical embalming starts by disinfecting the body with a germicidal spray and washing. Then you set the features by using a needle injector gun to get the wires in the maxilla and mandible to tie the mouth, or there are various suture methods. You close the eyes with an eye cap.
Vascular embalming will now begin. Typically, you'd be raising the right jugular vein for blood drainage and the right common carotid artery for the injection of chemicals. We have a fancy yet simple little equation to get the right amount of chemicals, but usually the firm you work for will have a set formula to follow for cases. You always note the condition of the body, and not really the cause of death because the condition of the body will dictate the HCHO (formaldehyde demand). A Machine is used to pump the preserves in, and there are many chemicals involved but HCHO is the star because it's the preserve.
Phase 2 is cavity embalming where you use a trocar to suck up all the fluids and matter from the trunk, then inject a strong phenol solution for preservation (hate that stuff like the plague!!). And of course, ya suture everything up at the end, rewash the body & dry,dress, casket, apply cosmetics, do hair... and there ya go!
I should note that this is a very simple 'normal' embalming stripped down and some details left out.. It can get much more complex depending on the conditions of the body. Multiple veins/arteries may need to be utilized, and you might need to reconstruct a face with mortuary putty. Uh... autopsy cases are never fun!!
I've actually embalmed people who died in the middle of surgery... the job can get to ya'! And we too are on call 24/7 like doctors because people don't die 9-5.
