As others have said, start as soon as you can.
The sooner your dcs associate sharing a book with closeness & cuddles, the better. At that age, they don't have to be very long stories either.
The sooner your dcs learn to treat books with respect (i.e not for tearing, walking/crawling over, throwing), the better.
It may seem a hard lesson to teach at a a very young age, but even toddlers can learn that throwing/stomping on their toys/books can "hurt" their toys/books and make both they toys/books and mummy feel very sad.
With all the rhymetime/story sack making & other activities run by libraries, there should be plenty of opportunities to introduce dcs to lots of different types of books that they can reach & choose from.
There are not just lift-the-flap and tactile books, but also books with the holes of shapes that can be fun for peekaboo, etc.
In fact, being able to make their own choice from various books & bring these for you to read to them is in itself a great game.
And for the days that you have no energy to be supermum/dad and do all the funny reading voices, there are CDs of books!
We especially loved the audio CDs of Dr Seuss stories read by Rik Mayall and Adrian Edmondson. Though we have the Dr. Seuss books at home, Rik & Adrian's version win hands down every time with their amazing voices and sound effects.
Generally building a bit of reading into your daily routine helps- not just at bedtime either.
- For example you could have a small book area in every room.
- Bath books are especially useful at meal times, as are the information booklets on child safety, etc that you often get from the library/GP.
It's never too early to learn the importance of holding hands, looking both ways before crossing the road, not playing with matches, etc. Also, if it's written in a book, it is the law - (great to exploit this for as long as you can).
- Besides this, don't forget that it doesn't always have to be a book, it can be cereal packets or road signs when you're out & about.
You could have lots of discussion about what else could "P" mean or what words start with P as well as the thrill of when your child recognises
the word "Stop", etc.
Books where they can join in at the end of the rhyme, or say a particular word (e.g. "puff") are good fun though after a while you may need lots
of patience with all the repeating & demands of "Again"/"More!"