Nearly anyone who has owned a pet has had to clean up after them.When they pee in the house on your new carpet, cleaning up can be a pain. While I by no means know everything on this subject, I figured that I could put what I do know out there. So really, this is more of a collection of ideas. Anybody who would like to add ideas, just comment, and I'll try and include them.
What I have covered thus far is cleaning carpet, linoleum (or other moisture resistant surfaces), and furniture.
A good example of a mess-making pet:
Step 1: Getting the Pet Out of the Way
First thing is to get the animal somewhere that if it to throws up again, etc. it won't make a bigger mess. Outside is probably best, but if it is still in the process of making a mess, the nearest easily cleanable surface is best (AKA, linoleum, possibly tile if it's not too porous). Once the animal is safely out of the way (make sure it's not free to roam the neigborhood so you have to go find it) the cleaning begins.
Depending on the surface, you might want to skip to a certain step.
Step 2 is on Cleaning Carpet
Step 3 is on Cleaning Linoleum
Step 4 is on Cleaning Furniture
Well, at least the dog is outside: