I have no experience with the minet package and I could not find any tutorial online but, the aracne function need a mutual information matrix (mim) which can be obtained with the build.mim function:

data(syn.data)
mim <- build.mim(syn.data,estimator="spearman") # syn.data is a data.frame containing gene expression data where columns contain genes and rows contain samples.
net <- aracne(mim)