Screenshot: windows key + shift + s
Quickly open any app on your computer: windows key to open your start menu, then type to search

Internet browser shortcuts:
new tab: ctrl + t
close tab: ctrl + w
move to next tab: ctrl + tab, or ctrl + page down
move to previous tab: ctrl + shift + tab, or ctrl + page up
focus url bar: ctrl + l
duplicate tab: (alt + d) + (alt + enter)

Please see Microsoft KB article on shortcuts you can use in Windows with your keyboard.