Here's a diagram that I print paged from the Ruger Manual..
The button must be in on the left side, then the spring, detent, while holding tention on the detent slide the magazine floorplate into possition till the detent snaps into the floorplates hole..
Hope this helps, A Picture is worth a thousand words..
Reassembly requires a certain degree of manual dexterity but don't worry because after you do it a few times, you will get much better. After you push the spring and plunger back into the mag, it will be under a good amount of spring tension so do not put your face directly over it in case you lose control. You do not want the spring/plunger flying out and hitting you in an eye. Also, be sure you put the button in the correct side: I found out it can be put in the wrong side.
I'll note first I posted a MKIIs magazine which is the same except for a notch cut into the magazine for the button release..
Also in the pics the top pic shows the direction the baseplate moves to remove & goes back in the reverse direction..
The second pic shows an Arrow but the floorplate doesn't go on that way, That's a Type Oed Pic right from the factory Ruger manual..
I disassemble my magazines every couple of range trips & lightly lube the follower plus spring & detents, Too much lube will attract rubbish from the 22 rimfire ammo & gum up the works..
I just aquired my 5th MKII & Have been without one for about 6 months now..
These 22 Autos are the Cats Pajamas as thier fun reliable accurate shooters & see more range time than any of my centerfires..
I usualy warm up at the range with my MKII & 10/22 before moving on to the centerfires, They give you trigger control..