Well it can be a bit difficult at times...
First of all, look at the permissions with
owngrpotr user group command
-rwxr-xr-x root bin vim
If the last/third triplet got an x ("can execute") in it, then others - and that means you - can execute it... If it's a shell-script or something like that, then others would need r ("can read") too.
If others don't got execute-permission but group (the second triplet) does, then you can execute it if you're a member of the group - in the example over, bin. For example, the wheel-group is often used to limit who may run
su, so only users belonging to this group could execute it at all. Another example is making a group for developers, and restrict execution of the C-compiler and such tools to this group.
If there is a trailing + after the last triplet, that means that AccessControllLists are used - this may add execution-rights to additional users and groups.
Even if you are able to execute the command, the command may depend on access to files, directories and/or devices that you don't have access to - this may limit what you'll be able to do (you may not be able to do anything).
Finally although you may be allowed to execute a command, the command itself may check your identity, and refuse to let you use it unless you're listed in a config-file or is certain users (eg. root). For example the
mount command will only allow root to mount any device - normal users are only allowed to mount devices listed as such in /etc/fstab... which may be none. If you're not root and tries to mount something,
mount will complain and refuse to mount the device. Another example is
sudo, which will run for anybody, but only users listed in /etc/sudoers will actually be allowed to run things as root.