First of all, go to your Blender floder and create there a folder called ‘Assets’,
Copy & paste your .blend file, in which you want to save your assets, into that ‘Assets’ folder you’ve just created,
Open your Blender and go to Preferences → File Paths → Asset Libraries,
In Asset Libraries section, click on ‘+’, then click on folder icon and choose the path to your ‘Assets’ folder you’ve just created from step ‘1’. Don’t forget also to give a name to your Asset Library, otherwise you won’t be able to save it,
Now, open your .blend file exactly from that ‘Assets’ folder where you’ve put it.,
In an ‘Asset Browser’ (see spoiler below), choose your folder from the drop-down menu, in my case I’ve called in ‘MAIN LIBRARY’, you can call it whatever you want (see step 4),
Summary
Now just choose your objects in an outliner window in the top right corner, RMB and click ‘Mark as Asset’,
When you’re done, File → Save and open another .blend project to where you want to put your assets from that one.
Repeat the step ‘6’,
Now it should works. Just drag & drop objects to your scene.