Well, the documentation is clear enough for me - once I realised that it can also be used for cropping and copying sections of images - though for some reason the documentation doesn't say what it returns.
I take it you've created an image of the right size with imagecreatefromjpeg() or whatever, and for the sake of argument we'll assume you called it $source_image.
I take it also you've created a 150x113 thumbnail image the same way, calling it $thumbnail.
You've obtained the size of the source image with getimagesize(), and got the width and height in $source_width and $source_height.
The dox say:
int imagecopyresized (int dst_im, int src_im, int dstX, int dstY, int srcX, int srcY, int dstW, int dstH, int srcW, int srcH)
and for the purpose outlined above, the arguments are:
dst_im = $thumbnail - the thumbnail image you're creating
src_im = $source_image - the image you're copying
dstX, dstY, srcX, srcY are all = 0 - we're neither cropping nor offsetting, so we want to start by copying the top-left corner of the source image into the top-left corner of the thumbnail image.
dstW and dstH are = 150 and 113, respectively - we want to fill the thumbnail image wall-to-wall.
srcW, srcH = $source_width and $source_height, respectively - we want to copy the entire source image.
In short: imagecopyresized ($thumbnail, $source_image, 0, 0, 0, 0, 150, 113, $source_width, $source_height)
Just one more thing to keep in mind: $thumbnail and $source_image are both gd_lib image handles, not files.