If you are an illustrator, I highly recommend having a simple portfolio website that you can use to display your work. When you’re querying, instead of attaching images (most editors and agents don’t accept attachments anyway), you can just send a link to your collection. Add new things, change out images in your rotation, and keep it clean, simple, and maintained. That’s about it. And if you’re not tech savvy, you may be able to hire someone via Elance (a freelance marketplace I’ve used to find web designers, or contractors in any arena, in the past) or in your circle of friends to put your image files (scans or digital creations) online. Just make sure that if you use scans, they are of high quality and taken under good lighting that’s true to your intended color scheme.
Two sites that I see a lot of illustrators gravitating to are Wix and SquareSpace. They are built to be user friendly and easy on the wallet. You can use templates provided or get someone to customize your site. These options are modern, work well across multiple platforms, and are easy to link to your other online efforts. I haven’t used either but I’m coming up on a project in my personal life and seriously considering SquareSpace because I like the design and functionality of their sites. I’ve been on WordPress for years and years, so maybe it’s time to try something new, minimal, and graphics-focused!
If all of this is very scary to you, you can just start a free Flickr account and make a gallery of your images. This is the bare minimum, and allows you to host your image and a description (I would opt for one if you can). Send links to the entire gallery in your query so that visitors can click through the whole thing instead of landing on just one image.
Many people overthink this sort of stuff because sometimes computers can be scary and the demands of building a platform seem overwhelming. Don’t let that stop you from putting up a portfolio. Hosting one online has become quite necessary these days, and agents and editors except to see several examples of your work, with different composition, subject matter, tone, palette, etc. (if possible), before they can decide if they’re interested or not.