[note: this is a work in progress. Some elements may change...]
The proper shiur that requires a Brocho Achrona depends on the type of food:
If the item is a solid:
The proper shiur is a K'zayis eaten within K'dei Achilas Pras
For the K'zayis of Brocho Achrona either eat less than 0.5 ounce or more than 1.5 ounces of food. Other Poskim say that a Brocho Achrona could be said on slightly more than 1 fl. oz. of solid food. [to be clarified]
According to some Rishonim a whole natural item [e.g. a grape] can also require a Brocho Achrona (even if smaller than a K'zayis). Therefore, one should only eat such items if he/she plans to eat a K'zayis. If not, one should break the item so that it is not whole.
K'dei Achilas Pras is an amount of time. Ideally, one K'zayis should be eaten within 3 minutes. However, a Brocho Achrona can be said as long as a K'zayis was eaten within 4 minutes. If a K'zayis was only eaten within more than 4 minutes a Brocho Achrona is questionable.
If the item is a liquid:
The proper shiur is a Reviis consumed within K'dei Shtiyas Reviis
A Reviis for Brocho Achrona is preferably at least 4.5 ounces. However, a Brocho Achrona can be made on slightly more than 3 ounces.
Because of a minority view that holds the proper shiur is actually a K'zayis: either consume less than a K'zayis for no requirement of Brocho Achrona, or more than a Reviis for an absolute requirement (in order to satisfy all opinions).
K'dei Shtiyas Reviis is the amount of time of consuming a Reviis (Poskim say it is no more than 2 sips with no more than 1 short pause in between).
Because there are some who hold that the time frame for liquids is the same as solids, one should make sure to drink a drop more than a Reviis at once, in order to avoid any questions. If one did not, the Minhag Haolam is to not say a Brocho Achrona.
Source: Sefer V'sein Brocho (ותן ברכה) (Addendum One)