Fastest Ways to Get XP

1. Be An Expert - Hardcore game modes will give you bonus XP for completing hideouts or other matches. The downside is you'll be using Expert aim so newbies might not fare too well.
2. Do Pike's Basin - Experienced players know Pike's Basin yields the most XP of the multiplayer hideouts. You can get around 2000XP and complete it under 7 minutes if you get good at it - which you will, by doing it over and over again. NOTE: This hideout has seen many XP "nerfs" where the amount you can get is decreased. The amount given above may no longer be true.
3. Kill EVERYBODY - Each non-playable character is worth a little XP. Authorities trying to subdue you after getting a bounty are worth more. Other players are worth plenty more. Take out each and every person you come across in the Red Dead Redemption landscape. A good Public Enemy run can give you a good amount of XP.
4. Pick Enemies Apart - For any enemy you come across, disarm them and shoot off their hat for a couple extra points. The downside is that this can be time consuming, especially with Expert aim. Sometimes Dead-Eye can pick out these spots automatically.
5. Chain Kill - Get extra XP from chaining kills together. For the newbies, it's the number in a green circle top-right. You have a short time to kill the next enemy and keep the chain going.
6. Complete Challenges - Every online challenge gives some XP. Stat challenges and Free Roam challenges have some easy ones to rack up XP. If you've already done them, you'll need to pass through Legend (level 50) to get them again.
7. Private Mode - For those who want to play in peace and accomplish some of the more meticulous challenges (such as complete a hideout without dying), you may want to switch to private mode and rank up in there. You can even invite your friends into the private session to help gain XP together.
8. Play During Double XP - Rockstar likes to give us double XP weekends here and there. Take part to level up twice as fast!
9. Play During Triple XP - Rockstar began running triple XP sessions almost weekly as well as some triple XP weekends. Keep an eye out for announcements of when it happens!
10. Play During Quadruple XP - A new thing for July 4th weekend (USA Independence Day), 2011. Possibly more of these to come!