I am posting an example from elsewhere to see if my understanding of interaction term interpretation is right.

      dds <- makeExampleDESeqDataSet(n=10000,m=12)
      dds$condition <- factor( c( rep("Ctrl",6), rep("Trt",6) ) )
      dds$genotype <- factor(rep(rep(c("WT","MU"),each=3),2))
      colnames(dds) <- paste(as.character( dds$genotype),as.character( dds$condition),rownames(colData(dds)),  sep="_"  )
      colnames(dds) = gsub("sample","",colnames(dds))

      #check reference levels
      dds$genotype = relevel( dds$genotype, "WT")
      dds$genotype = relevel( dds$genotype, "Ctrl")

      design(dds) <- ~ genotype + condition + genotype:condition
      dds <- DESeq(dds) 
      resultsNames(dds)
      ## [1] "Intercept"               "genotype_MU_vs_WT"      
      ## [3] "condition_Trt_vs_Ctrl"   "genotypeMU.conditionTrt"

# effect of treatment in wild type

      res = results(dds, contrast=c("condition","Trt","Ctrl"))
      # Here, the interpretation in straight forward (padj <0.05, and logfold change<1 for down regulated, and >1 for up regulated), and will be 
      resSig_trtvsctrl <- subset(res_D2, padj < 0.05)
      down_regulated_trtvsctrl <-subset(resSig_trtvsctrl ,log2FoldChange < 1)
      up_regulated_trtvsctrl <-subset(resSig_trtvsctrl ,log2FoldChange > 1)

#difference between mutant and wild-type without treatment? (this will be straight forward interpretationas well and extracting up and downregulated list as above?)

      res = results(dds, contrast=c("genotype","MU","WT"))

But for the below 3 cases that includes an interaction term, I am confused about extracting the up and down regulated gene lists.

#Effect of treatment in mutant

       res <- results(dds, list( c("condition_Trt_vs_Ctrl","genotypeMU.conditionTrt") ))       
       ix = which.min(res$padj) # most significant

                  baseMean  log2FoldChange     p-value    padj
        gene5102  18.690    4.757              1.60e-06   0.015

How do we interpret in this case because it includes an interaction term? Do we say gene5102 is downregulated expressed between Mutrt vs Muctrl? Although the sign of logfold change is positive, should I take the opposite sign for interpretation purpose? In such a case, how do I get the list of upregulated and downregulated genes

      resSig_MutrtvsMuctrl <- subset(res_D2, padj < 0.05)
      down_regulated_MutrtvsMuctrl  <-subset(resSig_MutrtvsMuctrl  ,log2FoldChange **>** **1**)
      up_regulated_MutrtvsMuctrl  <-subset(resSig_MutrtvsMuctrl  ,log2FoldChange **< 1**)

Similarly for

#difference between mutant and wild-type with treatment?

    res = results(dds, list( c("genotype_MU_vs_WT","genotypeMU.conditionTrt") ))

#different response in genotypes (interaction term)

    res = results(dds, name="genotypeMU.conditionTrt")

We have a section of the vignette that describes interaction terms in detail and provides a diagram.

If after reading over this section, they are still not clear, I recommend you consult or collaborate with a statistician.