They make knives that are designed to help prevent cutting into the intestines. A "gut hook", the small gap on the back edge of a hunting blade, is designed so that after you make a small careful incision, you can insert the dull part of the hook into the incision and slice open the hide without sticking the sharp tip of your knife into the gutsack... I got the SwingBlade from Outdoor Adventures. It works great for this purpose.
Nobody has really mentioned it, but if at all possible position the deer on a small slope so that gravity helps you out. I always start by cutting around the anus of the deer, then open the hide along the belly side all the way up to the sternum. If you want to do a shoulder mount, you need to be careful not to slice too much of the hide as you go forward. For a doe or something you don't plan on mounting, cut through the ribs as much as you can to open up the chest cavity. I like to sever the trachea as high up in the neck as possible, then use that as kind of a handle to pull down on as I separate the rest of the organs from the body wall. The diagphram is attached all the way around between the lungs/heart and the stomach/gut area. If you are careful and do it right, the whole shooting match shoudl come out all attached in one shot.
Some people like to hang the deer by the neck to help with this, other people hand it by the back legs... I prefer to field dress the deer on the ground with the back end downhill from the top end. Then I hang the deer for skinning and butchering.
And as always, the sharper your knife is, the easier the work is. I usually keep a stone with me so that I can touch up my edge if it's starting to get dull after cutting through ribs and pelvis... the saw idea is great. My dad has a small hatchet and a framing hammer... he'll bury the hatchet at the part needing split, then hammer it through like a wedge. It gets a nice clean cut, and it's faster than a saw.
"When a hunter is in a tree stand with high moral values and with the proper hunting ethics and richer for the experience, that hunter is 20 feet closer to God." ~Fred Bear