In Korean, to say “and” at the start of your sentence, use:
For example:
I am American. And I am smart.
I like cake. And I like donuts.
To use “and” at the end of a sentence in order to extend it, attach “고” to the verb stem.
The sentence above can be written as:
I like cake, and I like donuts.
You can also simply use commas to write the above:
I like cake, pie, and donuts.
When using “고” with two action verbs, “고” can translate to “and then” depending on the context.
I eat dinner and then I go home.
Or, more naturally, “I go home after dinner.”
To use “and” in the middle of a sentence, aka between two nouns, use:
Examples:
I want to go to Korea and Spain.
I like cakes, donuts, and pies.
과 and 와 can also mean “with” in some contexts:
I live with my uncle.