Random sampling is an archaeological term used for how they gather the 'evidence'.
Time, budget are all factors determining how extensive an archaelogist can investigate a specific area. To save time and money random sampling is implemented - which means instead of taking small samples of the entire area they take a sample every few feet or as determined (varies on the site.)
Once a site is located it is then gridded like a map and then it is determined where samples will be picked from. Gridding also helps in labelling so where the sample was found can be recorded and if need be later it would be easier to go back to dig more.
Below is an diagram of say a 50x50 plot that needs randomly sampled would be gridded.
a b c d
___________________
| x |
| |1
| x x |
| |
| x |2
| x x |
| |
| x x x |3
|___x__________x____|