Can someone tell me the basis of engineering a anistropic material?

Do you mean anisOtropic? It means that the mechanical properties depend on direction. For example tension in the grain direction or against the grain direction. Very strong in one direction but not so much so in the other.
That is a somewhat vague question. Do you have an example in mind? I guess it depends all on what you need.

I'll take a stab at it until an engineer corrects me.

First you determine design values for the material in question. to do this you push or pull on it in various directions from various directions until you have repeated it enough to be able to predict what will happen each time. Then you add a safety margin and you've got your design values.

Then you look at the structure in question. You'll need to take the design loads (loads the structure must be designed to withstand) and "apply" them to the structure to determine the load path -- lots of math or a specialized FEA program. Now you have the nature and size of the load on each member and at each connection. Now take the design values you determined and size the members and determine the appropriate connection.

Did I get it right?