Example: Consider $\{a,b,c\}\times\{a,b\}$ with the dictionary ordering. We get $aa < ab < ba < bb < ca < cb$.
In general to get a dictionary ordering on $A\times B$ out of two linear orders $A,B$ we do the following:
2. If the first coordinates are different, compare the second coordinates. If the second coordinates are different, use the ordering on $B$. If the second coordinates are the same, the elements you are comparing are the same (as they have the same first and second coordinates).
Example: Now my fellow sesquipedalians might be interested in the following linear order: Let $D = \{*, a,b,c, \ldots, z\}$ where $* < a < b < \ldots < z$ and $*$ stands for a blank space. Now consider $D^{189819}$ with the dictionary ordering. This will contain every English word both technical and non-technical. Granted it will also contain silly non-words like: “this*word*asserts*that*it*is*a*silly*word”.