It is so much easier to use a 3-button mouse: I just went and got a wireless one with a USB transmitter at my local drug store for about 10 bucks, and it makes using Blender *so* much easier. So while you can work around it, I would strongly recommend just giving in. Anything else is just going to be inefficient.
If you have a 2 button, or a 3 or 5 button. Except only the left and right click works.
Then go to User Preferences -> Input -> Click 'Emulate 3 Button Mouse' on the far left.
You can now hold down ALT while holding the left clicker down and panning the mouse around. You can also hold down CTRL+ALT to zoom in and out. ALT+SHIFT will allow you to move the entire scene.
If you also don't have a numpad you can turn on 'Emulate Numpad' and use the number keys instead of the numpad to get different views.