I was wondering if I copy someone else's software and make some design changes and try to make money from it. Is it legal?
Which licenses provides a facility for that?
Any license approved by the Free Software Foundation or the Open Source Initiative allows the software to be sold for profit by anyone, or used by anyone without restriction on purpose, including for monetary gain.
Note that you still must obey the terms of the license when selling other people's free/open software. The license will likely require that recipients must have the same resale and redistribution rights that you have, and it may require you to give your customers a copy of the source code as well.
The GNU project has an article about selling free software:
Actually, we encourage people who redistribute free software to charge as much as they wish or can. If a license does not permit users to make copies and sell them, it is a nonfree license.
Thus, any FSF-approved free license necessarily allows for-profit resale.
The OSI's Open Source Definition clearly lays out the right to monetize open-source software:
The license shall not restrict any party from selling or giving away the software...
The license must not restrict anyone from making use of the program in a specific field of endeavor. For example, it may not restrict the program from being used in a business, or from being used for genetic research.
Rationale: The major intention of this clause is to prohibit license traps that prevent open source from being used commercially. We want commercial users to join our community, not feel excluded from it.