There are a couple of different ways to store your dirty diapers until it's time to wash them. If you listen to the older people in your life, they're going to tell you that you have to soak everything in a bucket of water or bleach. Don't listen to them, you really don't want to do that. Can you imagine lugging around a huge bucket full of gross diaper water? This is where we take advantage of our modern conveniences. The method that I recommend is the wetbag method. Despite how it sounds, wetbags are not "wet." A wetbag is a bag made of waterproof fabric (usually PUL) that you put your dirty diapers into, and when it's time to wash everything you dump it all into the washer and throw the bag in with it. They usually have a zipper to hold everything in, but I've found that it's better to leave it unzipped so that everything can breathe and odors do not build up. They come in different sizes for different needs. You will want 2 "large" sized ones for use at home (one to use, one to wash) and a medium/travel sized one for when you're out of the house. My favorite brands are Diaper Palz and Rumparooz. Planetwise are also a good option, but I've found that they take longer to dry because they have cotton on the outside, and the cotton also tends to fade and look worn fairly quickly.
You can also use a trash can (with or without a swinging lid) with a liner, but the airflow would be limited so it might end up being smellier than a hanging wetbag. I have also heard of people just using a laundry basket, but that probably wouldn't be a good idea if you have curious pets or children. As with anything in life, try out a few different options and see what works best.