Log out and log back in in a world with less than 1000 people. This way, you'll be one of the only people there. Fighting moss giants with many people of a higher combat level can prove difficult. They will most likely see the drop and take it first.
Go to the Varrock Sewers. This is where most moss giants live. It also has many other monsters that drop valuable items, so this should be your number one choice. It has Zombies who drop coins, and two Deadly Red Spider eggs spawning on the ground.
Start killing moss giants. You can kill a few deadly red spiders who come near if you want, because they have lots of experience per kill. Pick up the items the Moss Giant drops (other than the iron arrows).
Once you have a full inventory, head to the Grand Exchange and sell the items. Big bones, deadly red spider eggs, nature runes, and law runes sell for hundreds. Bank any items that do not sell well and try again later.
Go to the Falador Shield Shop. Now you can sell the black square shields. These will not sell well in the Grand Exchange.
Go to the Varrock Sword Shop. Now sell the mithril swords. These will not sell well in the Grand Exchange.