I desperately need help! I've posted some pictures here to show you the extent of how bad it has gotten since I came back from Florida. I don't know anything about yard work, but I am an able bodied individual willing to work to restore it back to what would be considered sane!

I just recently got a mix breed puppy and it depresses me that we have a fenced in area that she could play in, but can't because the yard is too unfit due to possible infestation of spiders, snakes, poison ivy etc.

Help!

Wow, that is a lot of work, but I also see a potential paradise. I would protect myself (pants, boots, long sleeves, gloves, insect repellant) and do a walk thru, identifying plants (write it down!) Are there any pictures of this yard before it was overgrown? Use those as your guide. Clear out one section at a time and you will at least have a neater yard to work with.
Or you can have a clean up party: Invite your friends for a day of yard work--you provide all the dinner and drinks!

there seems a treasure trove of plants here, just hard to see what you have for all the volunteers and vines.....

start small and slow....
id any vines you don't want, take them off the trees and bushes.....
id vines you do want, and prune them back to shape....
id the ground cover that is weed, whack it back/or mow.
id the ground cover you want, prune back into the areas they were meant for....

as you disturb growth, you will see some fauna, frogs, toads, snakes, mice, etc....most of them aren't harmful....leave the garden snakes a corner somewhere the dog won't get them...they are good neighbors....(diamond-head poisonous, another matter entirely!)

after you've overcome the briars and poison ivy, the johnson grass, and winter weeds, you'll have a better sense of what is worth keeping.....

don't rush in and kill yourself with frustration, taking it in small bites, and long looks work better for this....maybe an hour at a time.....

What's wrong with it?

I agree with dlwenzel6 but would add three steps up front.

Identify dead plants or branches and remove those first.
Identify plant that are spreading out from one area to other areas and trim them back.
Trim low branches off of trees.

Once you have the obvious stuff cleared out, then you can work on either individual gardening beds or totally redoing the place.

Please post some before and after pictures for us.