Each tile is 256 pixels by 256 pixels.
Zoom level 0 is 1 tile. (1 x 1)
Zoom level 1 is 4 tiles. (2 x 2)
Zoom level 2 is 16 tiles. (4 x 4)
Zoom level 3 is 64 tiles. (8 x 8)
Zoom level 4 is 256 tiles (16 x 16)
The x and y counts are doubled for each zoom level. Per 88ad's comment, the formula for the number of tiles is (2^zoom x 2^zoom).
I hope you can do the rest of the math through zoom level 18. To save space, ocean tiles aren't stored. They're created as a response to the request.
At zoom level 3, the tiles are numbered from 0 to 7 in the x direction (longitude) and numbered from 0 to 7 in the y direction (latitude).
The tiles start on the American side of near the International Date Line (longitude -180 or +180). The tile 0,0 starts at about latitude 70 north.
See the Wikipedia article Mercator Projection for more details about how a sphere is mapped to a plane. The calculations for converting longitude and latitude to x and y coordinates are in the Wikipedia article.
You can map any point on the Mercator Projection to a tile set. A tile set is the set of tiles at a zoom level. You have to know the zoom level to know which tile set to access and to calculate which tile in the tile set to retrieve and display.
This blog post, Google Mapping, gives the formula for converting (latitude, longitude, zoom) to (x, y, zoom), where x and y represent the tile from the zoom set.