Your Neopets will never, ever die. So don't worry.
How to feed your pet: (other than Soup Kitchen)
1) Make sure you have food in your inventory
2) Go to your inventory (click on the number of NP you have and it should take you to your inventory)
3) Click the food. A pop-up window should appear
4) There should be a drop-down list on the pop-up window. Click that and select "Feed to ________" and click the button to the right of that.
5) The pop-up window should now say something along the lines of "_______: [insert comment here]! ________ was dying, and is now starving!" And a button that says "Close and refresh".
6) Click the button.
7) Repeat until your pet is full and / or you are out of food.