Scrapbooking can be as simple or as complicated as you want it to be. I think the first thing is to decide how you want to begin - traditional paper scrapbooking, Project Life-style scrapbooking, or digital scrapbooking. I do all three, but I started with traditional pages a bunch of years ago, then broadened out from there.
Project Life (known more generically as "pocket scrapbooking") is a simplified version of scrapbooking. Basically, you buy divided page protectors that have pockets which are each sized to hold a photo or a card/bit of memorabilia. So you print your photos, slip them into the pockets, fill in other pockets with bits and bobs from your trip (pieces of park maps, receipts, paper tix if you have any, etc - whatever is meaningful to YOU), use some journaling cards or paper to write down your memories, slip those into the pockets and boom, you're done. Project Life is a name brand for one company that makes the supplies for pocket scrapbooks, but there are a bunch of others now...
If you're on Pinterest, you might want to search there for something along the lines of "Disney scrapbook" or "Disney layout" and see what comes up - you'll get TONS of ideas, in a variety of scrapbooking styles. (Some are simpler than others, some are far, far more ornate. Take the ideas you like, and recreate them in your own way on your own page.) You can also search for "project life" on Pinterest to get a wide range of ideas as to how the pocket pages look when they're done. I've seen some really great Disney scrapbooks done the traditional way, digitally, and also in pocket-style pages.
If you want to stick with "traditional" scrapbook pages, you can easily find the things you'll need at your local big craft store - based on where you live, Michaels, AC Moore, Jo-Anns, Hobby Lobby, etc. If you're lucky, there will be a local scrapbook store near you, but those are very few and far between. You'll need to choose a size for your scrapbook (12x12 and 8.5x11 are the most common options), then pick a physical album. I strongly recommend 3-ring binder style albums, as it's so much easier to shift pages around and add/subtract pages. For inside the album, at a minimum, you'll need page protectors to hold all your pages, paper that appeals to you (ranging from simple, solid cardstock to fancy, elaborate patterned paper), a 12" trimmer for cutting that paper in straight lines, adhesive (acid-free is highly recommended, so your photos don't degrade over time) and as many or as few embellishments as you want to add. (Stickers, decorations made of chipboard/metal/wood/paper/you name it) There are also websites where you can find scrapbooking supplies, and often find better/more unique items, but shipping costs can get painful on some of the sites. Try scrapbook.com, or google scrapbook stores to get an idea of where you can shop online.
As another option, if you're reasonably computer savvy, you can scrapbook digitally. There are lots of software options that will let you do that. When I digi scrap, I use Adobe Elements. You can buy digital "papers" and "embellishments" that you'll then use along with your photos to create your pages. There are also templates you can buy that will basically allow you to drag and drop your photos, papers, and embellishments right in, and end up with a polished, professionally-designed page. There are even Project Life-style digital templates, so your end result looks like it was done in a pocket page, even though you did it digitally! In the end, you can decide how and where to print your layouts - either as individual pages which then go into an album of your choosing, or as a bound book.
Geez, this is turning into a HUGE post, and I could keep going! I'm happy to share some Disney pages with you, but I don't want to totally take over this thread. If you'd like to drop me a private message here, that might be a better way to continue.
The last thing I'll add here: It sounds like SO MUCH when you're getting started, but it's not really tough... and it can be lots of fun to scrapbook! Plus, it's such a good feeling to see your loved ones picking up your scrapbooks to go over the memories they hold. Oh, and the #1 rule of scrapbooking? Have fun!