Excavation is destruction. Once you disturb an archaeological context you can't put the soil back in the way it was, you just can't. If you want an archaeological monument or site to remain in its original state you just don't touch it. However, modern life goes on and very often a road or housing development finds that where they want to build is already inhabited by an archaeological site. So the development either bypasses the site, or, if thats too costly or impossible, archaeologists (hopefully) get called in to excavate it, what we do is called "preservation by record."
To give you an example, say I am working on a site with a medieval ditch (I'm from Ireland, early medieval ditches are probably the thing I've excavated most), we excavate in 'Sections' - I excavate the material that accumulated in my part of the ditch, say a 4 metre long portion, leaving a 'baulk' between me and the next person. At each end of my section I have a "section face" which, after I've excavated everything, I clean up and identify the different layers of soil (called 'contexts'). I then photograph and draw a scale drawing of this section face and take a soil sample from, maybe not all the contexts, but whichever ones we decide are needed (a more modern context at the very top with a coin from 1892 isn't going to get sampled, but the base context pretty much always will). If, while I'm digging, I find anything (ditches typically don't have a lot but you always find bone and maybe pins), I note what context it was in, if we have GPS equipment we'll zap the location if its important, and it gets bagged and eventually sent to be cleaned and conserved.
After all that, in Ireland, the law provides that the person with the License to excavate is responsible for producing a site report, which they must pay for (so all the dating, expert reports etc), the idea being that, during the excavation, we have taken note of everything we found in order to preserve the information that was in the ground. After all that the excavation material - finds, drawings, samples, etc becomes the property of the state and goes to the national museum. All the details will vary from country to country. I know in the UK they typically excavate 50% of a site in many cases, in France they dig sections slightly differently. The Artefacts typically end up in storage so they can be studied by future generations of researchers.
Thank you for taking time to reply. I have a few questions to follow up.
It seems like archeologists would be constantly busy trying to get to all the sites that are about to be built over. Does this make it difficult to do other more interesting but not endangered sites, also do you ever find yourself having to say no to an excavation for any reason?
In the case of burials will a body ever be exhumed studied and returned to its grave or a new grace?