This is the command line I used in order to obtain the up and down regulated genes, after extracting the differentially expressed genes:

up <- subset(resultsDEG, log2FoldChange > 0)

down <- subset(resultsDEG, log2FoldChange < 0)

I'd like to know if i'm doing this right because somewhere i don't remember i saw that setting the cuttof to 0 it's fine. But now i'm not sure if i should use a different cutoff instead of 0. I have 3 replicates per sample.

Take a look at the DESeq2 workflow, we go over interpreting the results including the LFC. Yes positive LFC is up regulation relative to the reference group.