If you are familiar with R, you could use the package "DESeq2", which makes it easy to do PCA and/or MDS. I used this toturial, however this seems also nice.

Using your count matrix and a meta data frame, which is created very quickly with this package, you get to your PCA plot in a few lines of code.

Figure 5, those are neither PCA nor MDS plots. Those are t-stochastic neighbor embedding (t-SNE) plots. This is a machine learning data-reduction method that is typically used for plotting high-dimensional data such as that from mass cytometry and other single cell data-types.

If you want to learn more about it (including how to implement it in R):

• Accelerating t-SNE using Tree-Based Algorithms (original manuscript)
• Playing with dimensions: from Clustering, PCA, t-SNE… to Carl Sagan!
• Comprehensive Guide on t-SNE algorithm with implementation in R & Python
• Visualization of High Dimensional Data using t-SNE with R

If you do just want to do PCA, look at my answer here: A: PCA plot from read count matrix from RNA-Seq