On your one year anniversary, that graph jumps up from zero to something like 20% vested, which looks like a cliff on the line graph. If you leave the company at this point, you get something like 20% or 33% vesting (depending on the number years til fully vested -- 4 years + 1 year cliff usually works out to 20% a year).
Beyond that, you basically step the graph up however many percent for each additional year.
4/1 is basically the silicon valley standard.
Usually you get the next increment on leaving (i.e. if you leave mid-month, you get the vest for that month), and often if you leave before a year (but after doing stuff, and amicably), you get some portion of the first 25% -- letting someone go after 11mo just to avoid the cliff is usually not done. If someone turns out to have been a bad hire after a month, it's more likely to just let him go and stick with the minimum terms of the contract (i.e. nothing).
IMO if you can't trust the management of the company, you shouldn't work there anyway. You should have contractual terms which are mutually acceptable, but it's almost always possible for an employer to exceed or fail to meet those terms, with limited recourse for most employees.
Edit: http://www.feld.com/wp/archives/2005/05/term-sheet-vesting.h...
Don't walk in there unprepared.
http://gigaom.com/2011/06/05/5-mistakes-you-cant-afford-to-m...
http://www.scribd.com/doc/55945011/An-Introduction-to-Stock-...
It is important also for other hires that are offered equity/options, so you will probably have to explain it to other people.