I agree, the PictureBox SizeMode property is the first thing you need to learn. It applies to the Image. The BackgroundImageLayout property applies to the BackgroundImage but can also be useful (for example for tiling).
But to make a new Image with a different size, for most purposes it only takes a single statement:
Code:
Dim resizedImage As New Bitmap(sourceImage, width, height)
The more complicated methods involving redrawing the image are useful when you want to enlarge the original with a higher quality than default. In that case you can use DrawImage in combination with one of the high quality Interpolation modes, Bilinear or Bicubic. Which of these looks best depends on the image itself. Bilinear can preserve linear detail better, but otherwise Bicubic is preferable. The low-quality modes can also be useful, for example NearestNeighbor (which enlarges each pixel as a square block and is also faster than anything else).
BB