You could create a "flag" variable for particular actors. Each actor would have their own column in your data and the column would have a 1 if the actor was in that film and a 0 if the actor was not in that film.
Of course, this creates lots of columns and can be tedious to code, but binary indicator variables can be really useful if you want to build a predictive model - worth it in my opinion.
actor1 actor2 actor3
movie1 1 0 0
movie2 0 1 1
movie3 0 1 0
Edit Re: Director/Actor
It is probably unrealistic to create a variable for every permutation of director/actor combinations. If you want to see how the variables interact you can code interactions into your model when you build it. If you were to do that in R it would look like this:
movie.predictor <- lm(suggestion ~ actor1 + actor2 + director1 + director2 +
actor1:director1 + actor2:director1 + actor1:director2 +
data = movies.data)
The ":" in R asks the lm(...) function to consider the interaction of those two variables in the regression problem, assuming you are doing regression. Don't worry the same ":" technique works across several model functions. Just read the documentation for your preferred language and package and look for how to code "variable interactions"
Of course, now you are typing out all of the permutations of variable interactions. You might want to also consider a clustering algorithm to group actors and directors together. I am not a movie expert but it seems like directors have favorite actors (and vice-a-versa) so I would expect there to be clusters of directors and actors with a little overlap here and there.