First, you need to repair and close off any outside access to the attic. Have your vents repaired/replaced and take action on any OTHER access points into the attic, like where a chimney might meet the attic, and so on. Many animals that make an attic their home can fit into an opening the size of a Quarter. So, in short, it's not enough to just repair/replace the 'obvious suspect access points'. You may need to do more. The best time to do it is during the day. Go into the attic and cover up any 'opening' (like gable vents and ridge vents) so you can see where sunlight is coming in. Then, block them off appropriately. When you temporarily cover any openings so you can see sunlight, and you have to do this from the OUTSIDE, that's fine too. Just be careful when you're on the roof or on the ladder.
Once you've done that, you may need to set some traps. Look for 'animal droppings' and nests and such to see how recent their activity is. Be SURE to wear gloves and a long sleeve shirt and long pants. A hat would be good too. Don't disturbe too much because your disturbance may look like 'recent activity' that's been done by the animals. Lift and set back carefully. You'll need to try to identify your droppings so you'll know if they're recent and if you need to trap anything. Perhaps for this part of the job, you'd consider hiring an Exterminator that SPECIALIZES in catching/killing animals in the attic.
Now that the openings are repaired/replaced and your attic is free-and-clear of any animals, you can now concentrate on replacing the insulation. Again, when you're working up there, wear long clothes and gloves. You'll need a mask that's rated for insulation too (depending on what type you have.) Insulation isn't something you can just put out into the regular trash in many municipalities, especially if they're still using landfills. Check w/your Hauler for info. Some contractors will remove it for you and dispose of it. If you're using batt fiberglass insulation, find out what's best for your climate and home. Do some homework on this front as well as the Installation Process. By investing some time in these things, you can save yourself some $$$ and spend your $$$ where it makes the most sense. (Like Extermination of animals and removal and disposal of the old insulation, perhaps.)
When insulating, you DON'T want to cover your vents. And you probably have some electrical lighting 'canisters' showing through the attic floor. DON'T cover them w/insulation. If you can, find out what type of cans you have and an Electrical Supply House, or mfgr., can tell you the proper way to insulate around, or on, them. There are light and HIGHLY expandable foams that you can buy for those 'tight spots'. READ the cans for guidance. Don't compress your insulation because it will loose its R-factor (i.e., its insulation ability.) If you have a floor up there, it's best to look into a way to 'raise' it just enough so that you don't compress the insulation. Pre-drill your holes and use screws to tie the floor down. You don't need that many of them to hold the raised floor down.
Of course, if you have more ?'s, post back. My best to ya and hope this helps.
Jay J -Moderator
PS: I'll be away this weekend but 'others' will be around ...