At a port or deck. Actually, they tie the boats to the deck/port, they don't tie it up.
bollard
Where boats etc tie up / dock
Where boats, barges etc tie up / dock.
Bollards
The western tie was called a bolo tie
posts
Not sure what you're looking for, but small boats can be "beached." Larger boats are "docked." A specific spot for one's boat can also be referred to as a "slip." Then there are places to tie up while afloat such as mooring buoys, rafts, and of course, you can always drop an anchor. Hope that helps.
War boats were called triremes.
The viking boats were called tall ships
The small boats of Venice are called gondolas.
life boats