We vaccinate our animals too. Still have to take them in for Rabies like someone above but it comes out a bit cheaper in the long run for not much effort.
And the one you linked to is a good vaccine. It protects against distemper, parvo, kennel cough (this is your adenovirus and parainfluenza), etc. It covers your bases.
One thing you need to make sure of is get your animals records from your vet and make sure your dogs aren't allergic to a certain vaccine. Some animals are allergic to some vaccines and your vet should have that on record if you've gone to them for a while and they've noticed anything. Course I reckon they'd of told you about it though.
As for actually vaccinating them it's fairly easy. The way we do it for dogs at the clinic is DHLP goes in the left flank, rabies goes in the right flank, and KC goes in the right front. This is so if they have an outbreak we can tell which vaccine they reacted to by where the outbreak is radiating from. So the point is to just remember where you stick them (and maybe avoid the right flank, I'm not sure if it's a standard practice amongst all vets, this layout of where to stick the animal, but meh who knows?) so you can watch it to see if anything happens.
Other than that just read the instructions, it should tell you how much to draw up, and a cc (cubic centimeter) is the same thing as a ml (milliliter) so if it's saying 'give 1 cc of fluid' and the syringe is in milliliters then it's no big deal. However some syringes come in 'units' which aren't the same thing. But I think that's mainly just insulin really. Never seen 'units' used outside of insulin.