Supplies: Slip cases for mags, recycling bin scissors, stapler, labeller.
Visit a dollar store for cardboard magazine holders. Many will have slip covers. These are perfect. Buy four. You can neatly label the boxes with an electronic labeler or computer. Hand printing looks sloppy.
First pass:
Remove the magazines from the shelves, drawers and storage etc. Stack them on the floor.
Honestly ask yourself what you really need from each and why? Are they for information or appearance? Choose the best ones only. Choose one area to keep them. If it takes more than one shelf then reduce. The rest you deal with now. It takes less time than you think. Dedicate it. Have fun.
Second pass:
Very quickly flip through the piles one at a time to toss away, right now, ones you can live without along with flyers and other loose bits. Place them in recycling bags or the recycling bin at hand. Create a keep pile for the magazines you want until the third pass.
Third pass:
Now is the real test. Choose a magazine & do the following: tear off the front cover and table of contents page for reference. Now tear out what you want: recipes, articles etc. DO NOT STOP TO READ. YOU HAVE A JOB TO DO!!
When you have what you need (including article endings on later pages) staple them together with cover and table of contents. Trim edges and ads off with scissors. Inset into box. Label the box "Magazines" (+ names of the magazines "Writer's Digest, Artist monthly, Housekeeping, Home repair, Car Digest" etc.)
Repeat. Be methodical. The blue bin will quickly fill up with ads, back covers, inserts and articles - clutter you didn't need. Feel a rewarding rush of achievement for each magazine done.
If you get overwhelmed, focus on one magazine. Relax and without thinking move on. Signs of being overwhelmed: exhaustion, headachy, need to turn off your brain or even the need to lie down.
Keep one type of magazine per case. The storage boxes will look neat and tidy and typically you will save more than three times the shelf space.