Haha, that's a question for the ages, and one that I've been planning to write up a decent answer to!
But to get you started... I'd say start with either Ender's Game or Ender's Shadow. They tell pretty much the same story, but are written from two different point of views. One is about Ender himself, and the other is about a character introduced in Game that Card wanted to write more about named Bean.
After you read those, you then can decide which character you liked more. If you want to follow Ender more, then you can go right to Speaker For the Dead. If you like Bean more (and wanted to know what happened to the rest of the characters), you start off with Shadow of the Hegemon. After those, it's pretty much straight-forward which books you go to.
The two series are:
Ender's Game, Speaker For the Dead, Xenocide, Children of the Mind
Ender's Shadow, Shadow of the Hegemon, Shadow Puppets, Shadow of the Giant, Shadows in Flight
Then there's the supplemental books to read. First Meetings is a collection of short stories, and is what it says in the title. It's stories about how some characters are introduced to others.
There's A War of Gifts, which is a Christmas story. But it's absolute fluff and not really that great, so don't worry if you can't find this one.
Then there is Ender in Exile, which takes place between Ender's Game and Speaker For the Dead. I would not recommend reading it between those two books unless you have already read the entire Shadow series.
Lastly, there's the First Formic War series: Earth Unaware, Earth Afire, and Earth Awakens. I haven't read those yet, but I'd guess you can read those after either Ender's Game or Ender's Shadow if you want a little history about the universe.
Ugh. I hope this clarifies a little bit on where to get started with this series. It is a lot to get through, but once you know where to get started (after Ender's Game and Ender's Shadow), it gets a little bit easier.