When two people finish eating and along comes a third person who is interested in combining for a zimun, he can, according to the following conditions:
The two could theoretically eat a little more if offered their favourite food.
The third person sits at their table and is given a k’zayis of food to eat (or a r’viis of drink, other than water).
The two have not yet verbalized “Let’s bentch” nor washed mayim achronim. (ShA1,2 – MB1,2,3 – BeH “k’zayis”) L’chatchila, offer this third person a k’zayis of bread (this doesn’t apply to the tenth person if there are nine people). (MB22) One person can combine with 9 others, two with 8, and 3 with 7 according to the above conditions and they can bentch with the Shem. Just make sure the leader of the zimun is one of the people who ate bread. (ShA2)
The people combining to the zimun must make sure to say their own appropriate beracha achrona after they finished listening to Birkas Zimun. (ShA3-MB15)
Do not be motzi anyone in Birkas Hamazon if you yourself aren’t obligated to bentch. (MB24)
Some poskim hold that you aren’t obligated in Birkas Hamazon d’oraisa if you didn’t drink and you feel thirsty. (Rama4)
If your stomach is full before you eat to the point that any more food would be disgusting to you, the food isn’t fit to bless upon, not before nor after – it is not called “eating”. (MB28)