How do I do it? And after I do it, is it possible to delete my current DE?
You can install Xfce with
sudo apt install xfce4 xfce4-goodies or you can install the base Xubuntu by:
sudo apt install xubuntu-core^
If you so choose and are using Ubuntu MATE and the MATE desktop you can remove it afterwards by:
sudo apt remove mate-desktop
I would recommend performing a backup prior to doing this. I would also recommend making sure your new DE is working before removing your current DE.
How can I know if my new DE is working?
If you can log into the new DE and everything works as you desire.
When you logout or reboot and you are on the login screen find the session button and hit the drop down menu and select the DE you want to login to.
Okay I got Xubuntu session and Xfce session? Are these the same? If so how do I delete the other one?
You could follow similar steps as above.
That really is beyond the scope of Ubuntu MATE support. Further Xfce and Xubuntu questions would be best supported via their various support outlets.
Out of curiosity, why would you do that?
Both DE are quite close in specs and philosophy, with Mate being more modern and actively developped.
My question is why installing another de and remove the current one when you can use xubuntu in this case?
I'm at the assumption that XFCE will make my pc peformance faster. Am I wrong?
Most probably, you would not find any difference in terms of performance.
Both environments are very light and with Mate you get a more up-to-date GTK environment and HDPI support, just to quote a few strong points.
If you are looking for an even faster experience, just change the window manager with the Mate Tweak utility.
On my hardware, Marco has always been the fastest, especially without compositor.
Okay thanks! I've changed it to Marco no compositor.