First time mom / ‘need advice

My baby is 3 months old and he’s strictly formula fed. No cereal or rice in the bottle just 4 ounces of formula every two hours. He’s starting to put everything in his mouth though especially his fingers which is causing himself to throw up sometimes. I give him tethers and he likes it but not as much as his fingers. Idk if it is because he’s starting to get to the age to switch to baby food idk I’m a first time mom when do I start introducing him to baby food or other food and how do I go about it?