Learn Russian: Они связали лодку и дерево верёвкой. - They tied the boat and the tree together with a rope.

The prefix с- often implies bringing things together. Связали means they tied the boat and the tree to each other. If you wanted to say they tied the boat TO the tree, you would use the prefix при- (implying attachment) and say привязали лодку к дереву.

Why isn't there a preposition like "с" (with) before верёвкой?

In Russian, the instrumental case on its own is used to show the tool or instrument used to perform an action. Adding с (with) before верёвкой would mean "accompanied by a rope," as if the rope were an entity helping them tie the knot.

Why does дерево look like it's in the nominative case instead of the accusative?

Дерево is a neuter inanimate noun. For neuter and masculine inanimate nouns, the accusative case (used for direct objects) is identical to the nominative (dictionary) form. It is accusative here, just like the feminine noun лодку, because both are the direct objects of the verb.

If I wanted to say they were in the process of tying them together, what verb would I use?

You would use the imperfective counterpart, связывать. Because the sentence describes a single, successfully completed action in the past, it uses the perfective verb связали.