Okay, so rather than give a step by step for MY build, since you all will have radically different budgets and parts, I'm gonna give suuuper general instructions operating on the reasonable assumption that you'll be working with a system that is a collection of separate parts rather than a pre-existing whole you need to take apart and that you have the parts you want to use already.
I'm also going to assume that you have the skills and knowledge for me to skip over stuff like "Hey, don't wire the power backwards!" or "Don't just cut wildly like a jackass!" and that you either have or know how to get wire and other stuff to hook all this business up.
Step 1: Parts.
Get all your parts out in front of you. Seriously. I'm not kidding. Your bike included. Pick up everything one at a time and really get a feel for the complexities of their size, shape, and weight. Look at where you're expected to put mounting screws.
If your speaker has a grille you can use, figure out how that mounts to the speaker. Does it just clip onto the speaker? Do the speaker mounting screws go THROUGH the grille first? Do you have to remove part of the grille before you can mount it or access mounting screw holes?
How does your amplifier mount? Screws? Can you get away with using something else, like wire ties, if you have to? Will velcro work? Does your amp have any fans or vents that need to keep unblocked? What about connecting terminals? Where are they located? Read the manual for your amp.
Pick up whatever battery you're going to be using and try holding it in your hands for a minute. An actual minute. Turn it over a few times and really feel where the weight of it lies. Is there any orientation where it feels happier sitting? How heavy is it, really? Where are the terminals? Picture how you would connect to them; what direction will the wires go from the battery?
How thick are the walls of what you're mounting all this stuff to? Does it flex a lot? Is it going to be hanging off of your bike or sitting on top of it? Will it be able to support the weight of all this stuff or will you need to add extra support? Do you live in a place where weather is an issue? Does one side seem more weather resistant than another? Think about how water might flow onto and off of it. Where would you run any cables in and out of it? Take the lid off and look at how the lid interacts with the interior of the container. Any latching mechanisms, rivets, or supports you need to be careful of? How much do you think you could reasonably cut away before the container starts becoming structurally unsound?
Now try physically positioning stuff against other stuff. Pretend you're working with cut out pictures of your parts and look at it to check fits. Put your speaker(s) on your container(s) and get a good look at where they naturally fit together. Now add your battery and see where that could go. Now your amp. Now turn your view around and see how they would fit depth wise into the container. Make sure you know exactly where everything ought to go.
Now take that mental image and think about where it'll go on your bike. How would you secure it? Would it bump into anything that moves? How much does all that stuff weigh and how much weight can your bike actually support? How would it affect the balance of your bike? Can you carry that much more weight and still comfortably bike?
This is all really important stuff we often forget to figure out ahead of time and then have to MacGyver solutions to mid-build. It's better to know NOW than have to learn later and possibly replace parts as a result.