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?
Use an old distro?
I first installed Ubuntu 4 or 5 on a Thinkpad T42 with 512 MB of RAM. I used it until about version 10, when they forced everyone to use left-handed window controls. It all ran about as well as XP did on that machine. Might be unsafe to bring online, nowadays, but if it gets borked do you really care?
You do not necessarily have to use an old distribution. In some ways, a modern one is even more efficient.
The biggest problem is the shift from 32 to 64 bit which makes the same software take 2 - 3 times more RAM.
Next is the desktop environment. KDE is surprisingly light compared to 4 but GNOME is a beast and KDE 3 lighter. KDE is still available as Trinity. GNOME 2 (still not that light ) is available still as MATE. Most of the X11 Window Managers from back in the day or still available and still as fast and light as ever.
A modern 32 distro with a decent DE is more capable than old stuff and almost as performant.
Check out Q4OS 32 bit with Trinity for example.