The cross legged position on the floor offers the great stability of a tripod (made by our two knees and the sitting bones of our backsides). Remember we sit towards the front edge of the zafu and allow our pelvis to drop forward, which, if we are sufficiently flexible, should allow our knees to fall towards the zabuton (you can use a folded blanket on a carpeted floor at home as an alternative to a zafu and zabuton). This stability allows us to make the upright (but not rigid!) posture with our upper body.
... And be careful not to try to do too much everyday at first, so as not to burn yourself out on it and make doing it a drag. The length of time we sit daily can be built up very gradually as we get used to it.
You'll find links to some info on stretches to help open the legs, hips and back HERE... and check out the 'How to do Zazen' link in the links section up on the right hand side of this page.