Take a look at your tarot deck. Divide the deck of tarot cards into the major and minor arcana. The minor arcana cards all have suits, much like a deck of playing cards. The suits in a tarot deck are wands, swords, pentacles and cups, or slight variances on those depending upon the style of the deck. The major arcana include a variety of images specific to your deck; however, the cards and their meanings are the same regardless of the deck you have chosen.
Consider the cards carefully, particularly the major arcana. You may find that you understand the meaning of the card from the symbolism of the image on the card. Some people choose to focus on a single card at a time during this phase. While developing some innate understanding of tarot cards and of the deck you have chosen is helpful when learning to read tarot cards, you will still need to learn how to put it all together to provide a useful reading.
Read about tarot cards in library books and online. While each deck is unique, they are all similar enough to allow any book on the tarot to be of use. In the case of reading tarot cards, there is really no one right answer and you will have to find the correct readings for each person within yourself. Consider bookmarking your favorite sites to refer to regularly.
Practice. The easiest way to learn to read tarot cards is to try and try again. Recruit friends or family and even just take the time to do readings for no reason at all. With time and effort you can learn how the cards interact with one another and the readings that make sense to you personally. Keep in mind that your interpretation of the cards may change based on the question asked or the person for whom you are reading the tarot deck.