find walks a tree and applies tests, which is the right tool once the rule is more than a name pattern: by age, by size, by type. Its syntax is unusual and its output is a list you can act on, which is where the power is.
About 1 min of reading
Find, preview, then act.
Make nested files
Before you run it, say out loud what it will print. Then open the answer.
Preview
Before you run it, say out loud what it will print. Then open the answer.
Act on the same rule
Before you run it, say out loud what it will print. Then open the answer.
A find from the root of a large tree can take minutes and touch things you did not mean. Start the path narrow and add -maxdepth when you only want one or two levels, so the search costs what the question costs.
-mtime measures modification, not access, and copying a file resets it. A rule based on dates is only as good as the history of the files, which is worth checking before trusting the set it returns.
find . -type f -name '*.log' -mtime +7 finds files, regular ones, with that name, modified more than seven days ago. Each test narrows the set, and order barely matters for correctness.
-exec rm {} \; runs a command per match and -delete removes them. Both are destructive, so run the same find without the action first and read the list it prints.
Piping find output into xargs breaks on spaces. -print0 with xargs -0 uses a byte that cannot appear in a name, which is the correct pairing whenever names are unknown.
Each one is defined here on this site. Open the entry for the full definition and the other words it points at.