Before anything else, you need to find some photo reference. The worst thing you could do is try to draw such a recognizable structure without the proper reference material. Even those who aren't experts will know if you just winged it.
The first step here is to lay down a verticle line in the center of the page. This is mainly a guide line. Next, draw two upward lines on either side of the image area. These are the base for the walls of the Colosseum. From the perspective of someone standing on the ground looking up, the outer walls are not perfectly verticle. Rather, they tilt inward and grow narrower toward the top.
The shape overall shape of the Colosseum is that of a cylinder. Check your reference. What you want to do here is lay down some curved lines that represent each level of the structure. On a blueprint, these would be straight, horizontal lines. In perspective, though, the lines become curved. Think of it like string wrapped around a paint can.
Looking at the reference material more closely, lay in more curved lines that run parallel to your previous guide lines. These are the framework for the various ledges, moldings and foundation of the building's various levels.
Check your reference. Some of the building's wall are still solid and straight, but others are broken and jagged. Start connecting those curves with the proper style of line. We're also indicating the thickness of the outer layer of wall, so the entire drawing already has a solid sense of shape.
This step is a bit tedious. Once again, check your reference before drawing. What we're doing here is laying down guide lines for all the arched openings that are a recognizable feature of the Colosseum. The openings on each level match up with one another, so you can't just freehand them.
Start in the middle with almost perfectly verticle lines. As you move outward to the left and right, your lines should start to tilt inward a bit. Always compare your line to the center, verticle lines and the curved/titled lines of the outer walls.
Some more technical drawing here, as we move on to the arches on top of all those openings you just blocked out. If you're doing this on the computer, there are a few techniques you can use to achieve these curves. I used the pen tool, but I could have also used the shape tool. Remember, you can always drop in an ellipse and erase the lower half to create an arch. If you're drawing by hand, you can either use a plastic stencil, or just try to have a steady hand. With pen and ink, I would lay down even more guide lines and then draw the curves freehand.
Go ahead and draw the inner part of the arches. This is where you really get a sense of depth in the layers of the structure. For the bottom of the archways, you're going to be using one-point perspective. To keep it simple, just remember that all receding lines go toward the center of the image. For a view such as this, that's enough to do the trick. You could go crazy laying perspective lines all over the place, but as long as you keep checking your reference and keep that center point in mind, you'll be ok. For more complex camera angles, however, a knowledge of proper perspective will be absolutely necessary.
No red lines here. Why not? For this step, you don't actually draw anything -- you erase! Your drawing has become busy with all sorts of guide lines and there's an overall sterile, blocky quality to the image. The first thing you want to do is go in and carefully remove all your construction lines. This will leave you with (hopefully) perfect archways, and you could just call it a day at this point.
We're not done, though. The Colosseum is really old and beat up, so you want to reflect that in your drawing. Now, this is where there's a difference of methods whether you're using the computer or pen and paper. For traditional drawing, you're going to want to ink your lines with a somewhat rough technique. On the computer, however, chances are you're going to have a very neat, sterile image. The solution is to go in and start cutting into your drawing with the eraser. As you start to shave away the smooth edges of your lines, the building will start to take on a new dimension. It's no longer a blueprint -- it's now artwork.
Adding details is my favorite part of drawing, but of course you can't do that without having your basic drawing done. If you've done your work correctly, this is the payoff. It's kind of like desert. You still want to check your reference, but you should be able to shut your brain off for a while as you noodle in all the little details and textures that literally transform your drawing. These are the things that will make people say "Wow, how did you do that?" Ironically, they're the easiest part of the drawing.
This is an optional step, depending on whether or not you want to color your image. If you're going to leave it as a black and white drawing, you should really go in and block in all the major shadow areas from your reference material. Double-check all your previous work and add details and texture as required. If there are any areas that look like flat shapes (but shouldn't), look at the general perspective of the surrounding shapes and drop in some appropriate detail.
The final, inked image.
The colored image. There are countless methods of coloring a line drawing. I just kept it really loose with the brush tool and had fun with it. You can rely on the drawing as it is, but you can also go in there and literally draw with the brush tool to flesh out shapes or add more texture to parts of the drawing. Try not to leave any huge blocks of color, because that will flatten out your image again.
That's it! You're done! Congratulations!