Gluing paper (assuming fiber-based photos) together for collages ain't rocket science. Cut and dry fit your collage pieces. I would hold them in place with small weights. I use washers from the hardware store for this purpose. Then pick up each piece and glue it down. I would probably only do two or three pieces before weighting down the collage (see below).
Most of my experience is tipping photos into handmade books rather than making collages but gluing two pieces of paper essentially the same in each case.
Apply a thin uniform layer of glue to the back of the photo, carefully position it on the other piece of paper and place under a weight for a while (maybe 10-15 minutes).
The right tools help. A glue brush is very useful, really essential in my view. For weights, a pile of all of those photo books you have hanging around works just fine!

I use thin sheets of Teflon (
https://www.amazon.com/dp/B07CWJZ5H7) to protect the books and the table under the pile.
Use a piece of scrap paper (or inexpensive newsprint paper, not a printed newspaper) under the photo when you apply glue to it so you can go right over the edge and not worry about getting glue on the table. Change this scrape paper after applying glue to each piece so that you don't get glue in places you don't want.
Personally, I avoid using Elmer's Glue for 'serious art'. It is not specifically marketed as acid-free. I imagine that if it was truly acid-free, this should be a selling point and therefore mentioned by Elmer's. Furthermore, I find that Elmer's Glue is also a bit less viscous that the fancier glue I now use. Of course, Elmer's Glue will certainly work is that is all you have got.
This is the glue I now use: Lineco Neutral pH Adhesive (
https://www.amazon.com/dp/B0016ZWEDY). It is a bit more expensive than Elmer's but still not too dear. I bought a quart (liter) several years ago and the bottle is still more than three-quarters full.
The right tools really help. I bought these two items and have been really pleased with them:
Glue 'Pot' (
https://www.amazon.com/dp/B095Q1RGHW)
Glue Brushes (
https://www.amazon.com/dp/B07FJX85SK)
The glue pot is a luxury, but a glue brush of some sort is essential. These items are made of silicon rubber and thus are very easy to clean even if glue has dried on them.