If you have some mechanical aptitude this might be easy but personally I don't rate this as an 'easy' job. If your car has a lot of miles it is best to replace the entire 'half shaft'. You will get two new boots (inner and outer) as well as a new CV joint with fresh grease. It will cost more but in the long run it's best because at some point the joint inside the boot will wear out and need replacing. Best to replace it all at once.
If you have some mechanical aptitude this might be easy but personally I don't rate this as an 'easy' job. If your car has a lot of miles it is best to replace the entire 'half shaft'. You will get two new boots (inner and outer) as well as a new CV joint with fresh grease. It will cost more but in the long run it's best because at some point the joint inside the boot will wear out and need replacing. Best to replace it all at once.
As best as I call tell from your picture, we are looking at the drive shaft from your transmission to the front passenger side wheel.
The object that you specifically point out is a rubber boot that completely encloses and protects a flexible "knuckle" type joint or a joint similar to what you see in a "universal" joint.
To the left of my picture sets the transmission or to be more precise, trans axle. The transmission turns the shaft to turn the tire and move the car.
This set up is what is commonly used in front wheel drives, all wheel drives or four wheel drives. In other words; this is how we make the front wheels pull the vehicle.
But, because the front tires also have to move up and down for bumps, and steer the direction of the car, this shaft has to have a certain amount of flexibility to it....
Thus, you have these flexible joints.
The boot is needed to protect the joints from being damaged from anything on the road, but perhaps more importantly, from sand, water, dirt and road grime.
If dirt and water were to get inside the boot, as it is with your old boot, the sand acts as an abrasive and causes very fast deterioration and wear of the joint. This deterioration occurs very quickly.
So it is imperative that this repair be made if you desire to continue to drive the vehicle.
No matter how you slice it, this is a pretty big job and not to be undertaken by someone who is not fully knowledge able on the topic.
I fear, that the damage has already been done, and in this case, it will require the complete replacement of the axle and all as an assembly. If the internal joint has been damaged, there is no getting around it.
You will feel damaged joints of this kind in the steering and moreover, hear them popping and cracking as well.
The extent of the damage is best left to someone who can actually get hands on the car, not me.
There is a product on the market for replacing the boot only. In affect, it is a replacement boot, slit down the side, so it can go over the joint. The sliced side is then glued and pinned together to hold in the grease and protect the joint. The ends of the boot are clamped tight to the axle.
A word of caution:
I have never, and I do mean never, seen this "replacement boot only" method work out as a long term option.
While others are certain to disagree, I feel that this is a clear case of a situation where it is far better to spend a little extra, use quality replacement parts and have a trusted certified mechanic to perform the work for you.
Unless you know how to disassemble a CV axle and replace that boot, it will be cheaper to replace the whole assembly.
The boots will cost at least half of a new axle price, and then you have to pay someone to overhaul the axles. It is not really easy, and is also very messy.
Look here and find axles for your car; http://www.rockauto.com/catalog/catalog.php
Just for fun, see what the price difference between boots and the assembly is.