Use 'Gimp' myself but I think the process will be very similar:-
Open 'explosion' as the background image
The spider image needs to 'Open as Layer' on top of the background
in the 'spider' layer 'Add Alpha channel'
Select white background of 'spider' and delete
All being wel that should work.
Needless to say try all this on a copy, not the original. I've got an old Photoshop 6 kicking about somewhere. I'll dig it out and check how it works with that.