It's free to create a goal with a Bright Red Line and start following it! If you're disciplined and self-motivated to reach your goal then Beeminder will never charge you for it. (Beeminder is obviously not targeted at people like you!)
Stay on the right side of the bright red line and all is roses and ponies.
Gallant is self-motivated. He's outperforming his red line and won't be paying anything for using Beeminder.
Goofus has crossed his red line. This will cost him dearly. (But derailing is not failing!)
If you cross the red line, that's when it gets interesting. It doesn't mean you'll be charged necessarily (you can sometimes choose to start with $0 at risk) but your bright red line will reset and you'll be back on the hook, and the amount you have at risk will go up. You can still choose to hit Archive on your goal and walk away at this point -- no further obligation. Maybe you decided you don't need Beeminder because you don't want to reach that stupid goal anyway. No problem! If you started at $0 then Beeminder will have been free for you too.
However, if you really meant to stay on track, and you want to keep going, at this point you'll have the threat of being charged $5 hanging over you.
(Again, it's always dead simple to walk away: Click "Archive" on any goal and a one-week countdown starts, after which you're off the hook.)
The goal of Beeminder's commitment contracts is to never let anyone derail on a technicality or due to genuinely extenuating circumstances. We explicitly ask you when you derail if you consider it a legit derailment. (If this sounds too lenient, look for No-Excuses Mode in the goal's commitment tab.)
You have to add a payment method to create goals but that doesn't necessarily mean paying anything, assuming you stay on track. What you do have to pay for is tracking more than 3 goals, which requires the Infinibee premium plan. There are other goodies and perks in the other premium plans. See also the first FAQ item below.