Boy oh boy do I love working with foam. I'm not sure what you're skill level is at so if I'm saying stuff you already know of if you need me to explain anything then let me know!
My foam process is this: I scale my template, print it out. I use regular copy paper, but to make tracing easier you may consider cardstock. I don't use it simply because my old laser printer cannot grab the ticker paper. I cut out the template using an exacto knife. If the template extends off the edge of the page, I cut out both pieces and tape them together.
Now that I have all of my templates cut out, I trace them to EVA foam. I use 12mm EVA foam floor mats. This is my go-to simple because they're easy to buy and they're rarely out of stock. Many folks choose cosplay-specific foam as it is more dense, often has less defects, and comes in a variety of sizes, but it costs more and takes time to be shipped. Being in Canada, it's also expensive to ship. That's why I go for the floor mats. I trace the template to the smooth side of the mat with a sharpie, being careful to bot let the template move while I trace it.
Then I use a 25mm and 18mm box knife to cut out the foam pieces. Make sure your blades are very sharp! You'll want to re-sharpen the blade every few cuts. You may be surprised just how quickly EVA foam dulls your blade. Keep the pepakura model open on your computer while you cut out the foam. Most of the cuts you make will have to be angled. I understand that there is a way to print out the numerical angle value of each cut, but personally I just eyeball it based on what I see on the computer. You'll get the hang of how much to angle your cuts as you get more familiar with foam. If you make the angle too sharp, you can always fill in the void afterwards with scrap foam. You will notice that some of the pieces in the pepakura file are not included. This is often because the armour piece is symmetrical, and you simply have to flip the template over and make the mirror side with your existing templates.
Now that all of the pieces are cut out, I like to sand them with the Dremel. Use a higher grit sand paper (120+). This will clean up and rough cuts you make and make sure all of the edges are flat for gluing. After that, I use a heat gun to seal them. Some folks prefer to seal the foam before they cut it as heat sealing can sometimes shrink those smaller pieces, but for the thick foam that I use, this isn't really a big issue. Once you've hit each surface with the heat gun, the pieces are ready to glue. If you need pieces to hold a curve, heat them with the heat gun and let them cool in the shape you want. They will then hold that shape, instead of trying to lay flat.
I use Barge contact cement to glue the pieces together. I find that this stuff is very strong. Apply contact cement to the each piece, spread it out with a scrap piece of foam, wait for it to dry, then put the pieces together. Make sure to wear an organic vapour respirator for this as Barge contact cement created fumes. Work in a well-ventilated area as well. You don't want these fumes going into the rest of your house. I re-inforce the seams on the inside of the armour with hot glue, just to be safe. Some folks use other brands of contact cement. I've tried LePage and it absolutely does not work. I've heard this is because it is water-based. I've heard some alternate brands are VL-2000, Weldwood, and LIDER'Z, but I have not tested any of these so don't know how well they work. Once the pieces are glued together, you may find it useful to sand down any uneven seams.
To fill the seams, I use kwik seal. It's a multi-purpose caulk. I put the kwik seal in the seam and then spread it out with a wet gloved finger. I do this to fill all of the seams. Some folks use foam clay for this step. I haven't tried it as it's more money and I don't really have any complaints about the kwik seal method. After this, I seal if with plasti-dip to get it ready for paint! Ive heard leak seal works for this as well. Again, I haven't tried leak seal as it's more money and plasti-dip hasen't lead me astray yet.
This is the general overview of how I make my foam armour. If you want to see how I made my whole suit, they check out the build video I posted on YouTube:
If you have any question feel free to ask me! Always happy to help