Everyone has given good explanations above. I will try to add some things that I have read and learned, that have helped me understand things over the years. Hopefully I won't confuse the issue more. First, in answer to your question, basically, to increase apparent depth of field (dof), you must either move farther back, use a wider lens, or decrease the size of the aperture (or sometimes a combination of the three). Note that the scales on your lens are very helpful in that respect, as well as for using the hyperfocal distance. Note also however, that dof extends about 1/3 in front of the object plane of focus, and about 2/3 behind it.
The reason the above works is due to those little beasties, circles of confusion (cc). That has always been difficult for me to conceptualize, much less explain. Imagine a very large format camera, with a film size about 4x6 feet. If you place one eye at the film plane, and look out at the scene through the lens, you will only see a small portion, a small circle assuming your lens' diaphram is circular, of the entire scene. You can't see all of it. Just what you can see out that small circle. Any place on the film plane that you move and look out, up or down, or from side to side, you will see a small circle of the scene. All the circles overlap, as you can tell by moving around. If you could reduce the size of the aperture while you looked, of course, the circle you saw would get smaller.
This is of course, also what your film would see (of course, it is stationary). Now let's get back to a conventional sized camera. Imagine you are looking at a point of light in the scene your are viewing. Those cc are going to be a lot smaller than in the imaginary camera above. They will be quite small on a 35mm camera. I don't have any books here, but I seem to recall that a cc on 35mm film must be 0.003 to be considered sharp (remember, we may enlarge it 10 or 20 or more times for our print). The larger those cc from the optimum (0.003?), the more blurred they will be. It was a small point light source, remember? So if they are too large, they will be blurred. They may be very slightly blurred, or greatly blurred. The larger the lens aperture, the larger the cc. The smaller the lens aperture, the smaller the cc.
A lens of one focal length might have a viewing angle of 50 degrees. One with an angle of view of 75 degrees (a wider lens) would cover more of the scene in front of you. It has to bring all that area into the same film size. So, it has to make everything smaller if you will. That gives smaller cc, assuming good resolving power. You probably need to get a book that shows ray tracing to see it, but those wider lenses suddenly have to send the rays at a greater angle to the film. That is what causes the so called wide angle distortion. As the rays get farther from the center of the lens, they get more oval. Actually, you can sort of see this effect with a flashlight. Focus it to as small a point in front of you as you can, then swing it to the side. You will notice the round circle getting more oval the farther away from directly in front of you.
I also said moving back would get more of the scene if focus. If you keep the object plane of focus the same, but move back, you are now taking in more of the scene. You can see more on the sides (and of course top and bottom) than before. It still has to get all that on the same sized piece of film. There will be a convergence of all the light onto that same size of film, so the circles will be smaller.
Well, as I said, I don't have any of my books with me, so I hope I haven't said something wrong. If so, somebody please jump in and correct me. Also, please understand the above is a simplification to relate to cc, not to explain all about lens design, which I know nothing about anyway. Some terms may not be exactely correct for other facets of lens design. Again, I was hoping to make cc easier to conceptualize. It still throws me sometimes, so between my own lack with words, and my own conceptualization problems, don't feel bad if it doesn't make sense. :bang:
