The default size of the slideshow images used on the homepage is 950px wide by 290px high.
You can change this with 2 steps. For the purposes of this post, suppose you want to make the images 400px high.
Step 1. Settings
In Theme > Template Editor open settings.html and scroll down to where the slideshow images are defined. Change the dimensions for each image.
Save the file then close it.
Step 2. CSS
Now open styles.css.liquid and find where "#banner" is defined.
You will need to set the dimensions in two places: #banner and "#banner .images".
Note: The gradient and border shadow take up space, so you need to add 10px if you are using them. In our example, we would set them to 410px.
Save the file and close.
Now you should be able to upload your new images in the settings area and they will appear at the new size.