The Daily Ladder for League of Legends can be found on the overview page for League of Legends.
To get there, click League of Legends in the left menubar called Your Games.
While at the League of Legends overview page, scroll down slightly and you will be able to find a big banner for the Daily Ladder.
Click the turquoise Play button located on the banner.
See the ladder by clicking on the item Daily Ladder and you will automatically join the best Ladder for you based on your highest ranked linked Summoner. (If the Daily Ladder Play button is grayed out it means that your Summoner is unranked or that you haven't added one yet.)
Join the ladder
Once you have joined the Ladder you can't leave it or join another one until the Ladder has closed. You can see how much time remains on the daily Ladder Overview located on the right side.
Play 3 Games
To get a position in the Ladder, enter the League of Legends 5v5 Solo/Duo Queue with the Summoner you have joined the ladder with and play the first game.
You can play as many games as you like during the length of the Ladder, but only the 3 best games will determine your total score. In other words, if you have played 6 games during the day, the 3 games with the highest score will count towards the total number of points you get and your final placement in the Daily Ladder.
If you see this message:
You need to verify your Summoner (to show that you are the owner of the League of Legends account) before you can play.
Once you've played a few games, your position and status will update automatically to reflect your current score.
How does the scoring work?
The current scoring is described in the bottom right of the Daily Ladder view. In short, winning games and getting kills, assists and gold will give you points. The scoring may change as we improve and update the Ladder. Learn more about the scoring method here.
Please note, you need a ranked Level 30 Summoner to join the Ladder.