How about drawing a card a day? Old technique, but very useful for getting a feel for what the cards mean.
If you're a night person, then evening works best, if you sing in the morning, then that's when you're more alert.
How to? Pull a card, or go in order--it's up to you. Spend a few minutes really looking at the card. Colours, figures, images, backgrounds. See if anything in the card jumps out at you. Sometimes it will, sometimes it won't. You might want to write everything down--both the images and any feelings you have about the card--having a notebook that you can add pages to is useful, but any journal where you can keep your thoughts organised and have a section for each card works.
If you've got a card easel or somewhere handy, you might want to leave the card out for the day. At the end of the day take a look at it again, see how its energy has played out in your life. Again, write it down.
I'm sure other people will have other suggestions, and by all means, start reading about tarot, too--here, in books, wherever.
As for readings proper--when you feel ready. Let people know you're starting out, but probably best to avoid anyone who's overly superstitious and might take every word as holy writ--or trade readings with other people who are learning (which is probably everyone who reads at all, because the learning never stops).
There are no real right or wrongs, but I've found that the card-a-day really does help you get to know a pack of cards--as does writing down your reflections. Have fun with it, too--don't feel like you need to memorise everything overnight, that's just overload.
Personal opinion: Depending on what part of the world you live in, it's probably best to start with a Rider-Waite-Smith or very close to it reworking, or a Marseille, as those are the most used for readings, ergo, have the most information and other users available for advice.
Good luck!
MM