The core parts we picked up were "Only do for me what I can't do for myself" and "Help me do it myself". So what does that mean and what does that look like? 
-"Only do for me what I can't do for myself" means if your 2yo can put on her own shirt, stop "helping". Sometimes it can mean getting dressed takes longer... but in a short while it will be faster since you know have one less person to put a shirt on! Plus, the 2yo is excited and proud of herself for putting on her own shirt!
You would be suprised the things that a small child can do. I remember being fairly shocked at other moms who were wondering if their pre-teen COULD do chores (not should, that is a family decision). I was shocked because of how much Lil'K can do, I didn't realize how far off the norm we are. When it comes to her I basically try and stay out of her way. She was reading by 2.5, and at 5 she can wash dishes, sort laundry, start laundry, do basic addition and subtraction (partially self-taught), and fold her laundry. She really confused us by how much she just DID.
Once Lil'C started to learn things (although Lil'K usually does them first) we do the same. He can now dress himself, excluding his shoes and right sock. He can sort laundry, put away his clean clothes and is AMAZING at math and spelling (seriously spells better than me)
-"Help me do it myself"
This was really HUGE for Lil'C since he has the deck stacked against him with Cerebral Palsy/Right Hemiplega. For Lil'K this was basically stools around the house, so she could reach things and low shelves for kid dishes.
For Lil'C I basically have to break any skill down and teach him how to do it one handed. I usually put my dominant hand inside my back waist band and learn the skill, then teach him that skill. I also teach each sub-skill one at a time until he can do them all Independantly.
Putting on his shirt for example. First we worked on putting an arm through the sleeve. Once he could do that part independently we figured out he could pull the shirt over his head if he had the right arm over his elbow. Once that part was down, I found he could get his left arm in his shirt once the right arm was in, followed by putting the shirt on his right arm. Finally I got him to put his shirt on if it is laying flat face-up on a surface (table/couch). He spins it mid-dressings so if it is face down it will end up backwards. The step we are currently working on is getting it onto that surface himself and how to turn it right-side-out if it is inside out. This process has taken MONTHS and has required help from occupational therapy.
Because we have done this with almost every skill, I can now dress myself, tie my shoes, put on my socks, open a jar, cut food and fold clothes.. all one-handed.
The other part is tools. We have a one-button battery-operated can opener, but we will likely get another.
We also have a button-puller but haven't used it much yet. We searched for a power wheel that could be driven one-handed, which Lil'C loved until Lil'K and Baby K filled it with mud... electronics are not fond of mud.
Montessori is also big on emotional regulation, which means to respond calmly (Positive Parenting works well with this but I'm still learning..) which when I manage to do certainly helps. With Daddy C and I both having ADHD (meaning all the kids will/do as well) then this can be important, yet difficult, to do.
Lil'C has become much better at calming, although his frustration (usually at Lil'K) can get the best of him.
Montessori also pushes for lessons/trays/items to be self-corrective. A puzzle would be a familiar example. A puzzle can only go together one way, so if you put a piece wrong either the piece will not fit or you will he unable to finish.
What philosophy do you use? And why?