If you want to strengthen and tone your stomach, there is no need to do gym or buy any ab machine. There are many abdominal exercises you can do at home without using any equipment.
The video below is a good example. This is a 10 minute abdominal workout which includes various ab exercises you can do at home and these train the core muscles efficiently.
Do this routine 3-4 times a week, (once - twice a day) and you will see good results with some extra cardio and proper diet.