Just about everyone will have a different answer, I think.
When I started, I bought Joan Bunnings tarot book (not the Big Book of Tarot but a much earlier book) and a deck of Rider Waite cards. I found it very challenging to learn using Bunnings book because there was too much to learn.
I muddled my way through by doing simple readings (which I found on the internet, mostly). If I couldn't work out the meaning, or a card didn't make sense, or didn't resonate, I would then google lots of different meanings to try and learn and make sense of the cards. I found that quite useful to learn the basic traditional meanings, as well as what meanings other readers ascribed to cards, and then I started using a journal, putting in the meanings of the cards as I learned them.
I also found internet forums quite good for learning, especially the Spiritual Forum, which is where I came across 55Degrees and a few other very good readers who were helpful in the learning process.
The best way to learn the cards is to practice, practice, practice. Don't overwhelm yourself with too much information and spreads which are too complex. The old adage of "Keep it simple stupid" is probably the best way. Start small and build from there. Once you have a groundwork of the traditional meanings, then you'll find your intuition will kick in and you'll find more meanings that are personal to you. Some readers don't worry about book learning and just read what they see in the cards. Although that method surely works for some, I personally found it important to learn the traditional meanings first, so I had a solid understanding of the cards.
A couple of sites I found good in my early journey are the Daily Tarot Girl and Tarot Avenue. Both sites have free resources to learn the Tarot and they are both down to earth. Be careful not to go onto too many sites to learn initially, or you will just find yourself at loggerheads and overwhelmed. Try one at a time that you feel may resonate with you. David from Tarot Avenue offers a free Introduction to Learning the Tarot which you may find useful. Kate from Daily Tarot Girl offers some free videos as well. It's important to find someone that you feel comfortable with, as far as their style of teaching, readings, etc, and that you gel with their personality.
Above all, learning should be fun! Enjoy the process and don't put too much stress on yourself.