Well, most of the directories and files have 755 as the default so I would start there to allow you to execute common utilities. You can then later figure out if you want to tighten security.
sudo chmod -R 755 /usr
This page has a variety of ideas, depending on what you have access to. Example, if you have execute permissions on
cat you could use the following sequence of commands to "copy" permissions from another file (in this example
/bin/cp /bin/ls /tmp/chmod
/bin/cat /bin/chmod > /tmp/chmod
/bin/mv /tmp/chmod /bin/chmod
Notes: The first commands copies a file (including permissions). The second command copies the contents of chmod to the new file (does not overwrite permissions). The last command overwrites the original chmod file.