Basics and Details
The initial thing to understand is how the stat lines have changed. While the game itself only has four pages of rules, the real meat is going to be in the individual unit entries known as Warscrolls. Any unit only has four actual stats, listed in the characteristics circle on the left hand of the scroll. These include movement (how far the thing can go), wounds (how much pain the thing can take), save (how well it is able to shrug off damage), and bravery (how likely it is to flee in the face of adversity). These stats all interact with the core rules of the game and fit well enough within that framework. What makes Age of Sigmar special and each unit unique is what can be found on the rest of each warscroll.
It behooves me to point out that some claim a GW rep has been going around and saying that these 'fun rules' such s tipping your fedora'd chalice to m'lady to get rerolls is just an homage to the old fluff and a light-hearted sendoff to the old models line. You will notice that the compendium warscrolls are not listed as 'Ogor Kingdoms' of "Orruks and Grots', meaning that these are NOT the new forces we will be seeing in Age of Sigmar, but rather short-term rules to use our old models in until we see the new things that will replace what we currently are using. A good thing to notice is that the rules for the box set don't include anything remotely like chanting things in a heroic voice or having a dance-off, indicating that if those types of rules aren't up your alley, you only have to wait a little longer for them to phase out.
Everything in the age of Sigmar is technically 'unbound', to borrow a term from 40K. You can take whatever you would like, and use any models in your army. You can have as large of units as you like, and take as many models as you want without regard for what your opponent is bringing. You of course have a disadvantage built in for taking 1/3 more models than your opponent, but if you outnumber then by enough then you are unlikely to lose via the sudden death rules. The advantage here is bringing a million models to the table, which boosts sales, so that makes sense. Alternatively, you can bring a small number of elite units, say, populate your entire field with giants, dragons, greater dameons, and the like, and model for model not outnumber your opponent while still greatly overpowering them. This will also drive sales of big expensive kits, which makes sense. I've written before about how GW exists to make a profit, but we need to be mindful of what makes a good, enjoyable (maybe even competitive) game vs what makes you win every round. the quickest fix is to try not to be a terrible opponent, but you could also attempt to roughly match wound count rather than model count. Obviously this isn't perfect, as 14 wounds of skeletons isn't equivalent to 14 wounds of Bloodthirster, but it's better than assuming the skeleton force is 14 times stronger, don't you think?
your playstyle is always a win in my book. Generally speaking this ruleset seems more suited to smaller games and lower model counts, but you can always wage war on an apocalyptic scale as we did back in 8th whenever it strikes your fancy.
How has Age of Sigmar been going for you so far? Has it been enjoyable or frustrating? Let us know how it has been working out.