Doy la naranja a mi perro
 

What is the everyday conversational way of saying:

"I give the orange to my dog."

Would it be:

- "Yo doy la naranja a mi perro"
- "Doy la naranja a mi perro"

Or is it something completely different?

The last sentence you wrote is correct.

Adding 'yo' emphasizes that the speaker did it (as opposed to someone else).

It is more common doubling the indirect onject :

Le doy la naranja a mi perro (very common)
A mi perro le doy la naranja ( compelling the use of the IO)
A mi perro se la doy ( le-la = se la) la = naranja.