Letter bonuses multiply a tile
Letter bonus squares usually affect only the tile placed on that square. A double-letter or triple-letter square is most valuable when it catches a high-value tile, but it can also matter when the tile participates in a cross word.
Word bonuses multiply the whole word
Word bonus squares apply after the letters in the word have been counted. If a move covers more than one word bonus, those multipliers can stack. This is why board position can matter more than simply playing the longest word available.
Bonuses usually count once
Existing tiles on the board generally no longer activate their original premium squares. A solver has to know which tiles are already fixed and which tiles are newly placed before it can score a move correctly.
Cross words can quietly add points
A play that forms two or three valid cross words can beat a flashier main word. TileSmith scores the main word and cross words together so those small overlaps are included in the final move ranking.