Yes, keep it simple. If the child is under 5, you might consider just having a family dinner or lunch. You can do a cake, some balloons, a few presents. If the child has one friend that they are close to, you might invite him/her to join you for the meal.
If they are school-aged, consider what their interests are when you select a "theme" for the party. However, get a handle on the guest list, your budget, etc., fairly quickly or this event will blow up in your face.
You don't need to spend a bunch of money for the kid to have a good time on their birthday. You don't need to have favor bags for everyone. You don't need to hire a pony for pony rides.
Have some games for the kids to play - Tag and Hide and Go Seek are good ones for younger kids. Have a cake or a great big cookie, some lemonade and call it good. All the child needs, really, is to know they are loved.