I know how to do cutouts, but how can I put all the images I want to use on a common background and then arrange them in the way I want?
When you have created the clipped images save them as psd-files.
Then open (or create the background) as a separate file and use File > Place Embedded to place the images as Smart Objects.
With Edit > Free Transform you can scale, rotate etc. the individual images and in the Layers Panel you can change their position in the stack.
As Smart Objects the transformations are calculated on the basis of the original each time one changes them, meaning that if you transform the images again (and again …) the damage does not cumulate.
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Start off by deciding the size you want your poster to be. If it's going to be viewed from a distance it can have a lower resolution. Say 200ppi.
So if your poster is to be (say) 20 x 15 inches, the pixel dimension (in this example) would be 200 x 20 by 200 x 15 = 4000 x 3000px (You might want to make it slightly larger if you're going to add bleed to the edges.)
Place your cut-outs on his space and move them around to suit your design. A separate layer for each image.
Work in RGB color mode,
Make save incrementally named copies as you progress and keep a copies of the PSD file externally.
You might want to save a copy in another format for printing, perhaps JPG or PDF, always keep your layered original PSD file so you can rerturn to it to make further changes .