The classical approach would be to use PCA (Principal Component Analysis) in order to perform a linear dimensionality reduction. Essentially, this projects your data onto a lower-dimension space (in the 2D case this is simply a plane) while preserving as much of the variance of the data as possible.
Running PCA usually involves executing a single command in most programming languages, so it is very simple.
You should remember that it is possible that your data cannot be accurately represented in 2 or 3 dimensions. PCA will automatically give you a quantitative estimate of this: It will tell you what percent of the variance is captured by the resulting low dimensional representation. This will give you a feeling of how much information you lose by looking at this simplified visualization.