I had an Aspire One D270 laptop with a 32-bit Intel Atom CPU and 1 gigabyte of RAM, so I installed Debian with Xfce on it, but even then it's running way too slow.
Is there anything I can do to make the laptop faster and more responsive given its limited memory?
JWM is my suggestion. It's a floating window manager (not tiling) that doesn't require almost any knowledge or key bindings to use and it has all necessary stuff included out of the box afaik. You can also use xdgmenumaker to make the right click/Start menu better.