Are there things I can do for gastroenteritis at home?

Fluids. Gastroenteritis is usually quite self-limited and you should recover quickly from most causes. Keeping hydrated and replacing electrolytes may be helpful. If nausea is not too severe, cola may help to ease this. If it persists beyond 24 hrs or you cannot keep anything down see a doctor asap.
Yes. Start w clear liquid like water, slightly flattened soda that is clear, or sports hydration drinks. Sip, sip, sip. Work up to solids w bland foods like bananas, rice, applesauce, toast, gelatin, or chicken. Avoid alcohol, nicotine, caffeine, dairy & high fat foods. Rest.