There is only one blessing ordained by the Torah. That is the Birkat Hamazon (Grace after meals), as it is written: "You shall eat, be satisfied, and bless..." (Deut. 8:10). Oral Tradition teaches that one need say Grace only after a meal with bread, as only bread truly satisfies. The Birkat Hamazon consists of four blessing; one for the food, one for the Land, one for Jerusalem, and one giving thanks to G-d for His kindness. The exact wording of Birkat Hamazon differs from community to community, but most communities have greatly "padded" these blessings. The original, short version has of late been popularized by Rabbi Yitzchak Abadi. Birkat Hamazon must also said on bread-like foods such as cake, if eaten in quantity. What is meant by "in quantity" is a vast topic, with many opinions.. A qualified rabbi should be consulted.
Foods not in the bread camp, but still of great value, like grain dishes, wine, or the five fruits that Eretz Yisrael is blessed with (grapes, olives, dates, pomegranates, figs), get a mini Birkat Hamazon, containing all the themes of the large Birkat Hamazon in one blessing. Whether this blessing is of rabbinic or Biblical status is a subject of dispute.
For other foods, a short, one line blessing called "borei nefashot" is said. It is not only of rabbinic origin, but came in quite late, to the extent that some consider it optional. A devout Jew will be careful to say it. All of the above blessings can be found in any traditional siddur (prayer book).
A major difference between the blessing before and after eating is the quantity needed to require a blessing. The blessing before is said on any amount, as we are blessing for the pleasure of eating and drinking.There is pleasure in one raisin or in a taste of ice cream. The blessing afterwards is for the "satisfaction" which only comes with some quantity. The minimum quantity for saying a blessing after food is an "olive's bulk" (k'zayit). How big that is is also controversial. (Some imagine that ancient olives were the size of an egg or more).Most Ashkenazi rabbis say about 1 oz. (29 g.),(some double that!) whereas most Sepharadic rabbis privately say much less; little as 5 g.) but rarely will say so publicly,for fear of denunciation by Ashkenazim. For liquids, an after brachah is required if a "revi'it" is drunk. This is estimated to be just under 3 oz. (86 ml), but is probably less. Some Ashkenazi rabbis double this as well..