Firstly, make sure you hydrate yourself since vomiting upsets your electrolyte balance. Coconut water is very good. Herbal teas such as chamomile and peppermint (brew a teabag of each) are very soothing on the GI tract and decrease irritation, spasms and inflammation. Lemon & ginger, with perhaps some honey (if you eat it) is also good. Ginger particularly is also anti bacterial and anti-emetic (stops vomiting & nausea).
Bone broth is probably the best way to shuttle in nutrients if you can't keep anything down, and the gelatin is very soothing on the GI tract.
Once you actually feel hungry, well-cooked lean meat (e.g. turkey breast), root vegetables (carrots, parsnips, swede, squash, pumpkin) and some fruit (cooked apples/applesauce, bananas -if you eat them) are best. You can boil some turkey/chicken breast with some root vegetables in some bone broth, and puree for a creamy soup. Similarly, you can cook & puree root vegetables and even cauliflower to make a mash.
Then you can go on to steamed lean-ish meat, perhaps some scrambled eggs.