This is an explanation on how to do a simple Ganesh puja at home. Please note that this puja procedure is only to give an idea and you can be flexible in your Ganesha Puja.
After taking bath
Take the blessings of Lord Ganesha by touching the feet of murti or portrait. Ask Ganesha to help in make this puja a success.
Remove all the puja items you used the previous time. Clean the murti or painting of Ganesha.
Take very little water and sprinkle it on the murti and on you for self purification.
Keep the lamp ready. Use cotton to make wick. Pour oil or ghee or mustard oil or any other cooking oil in the lamp. Dip the wick. Dip the wick and squeeze to remove the extra oil from one end and project it outside to light the lamp.
Keep incense ready.
Keep red flowers ready. If you have Durva Grass offer it.
Keep a single banana or a fruit or a piece of coconut or a sweet ready.
Keep sandalwood paste or red kumkum ready
Light the lamp. Offer your prayers.
Apply sandalwood paste or red kumkum on the forehead of Ganesha.
Burn the incense.
Offer the fruit or sweet.
Take some sandalwood paste or red kumkum and apply it on your forehead. To apply means to make a small mark on the forehead.
Listen to a prayer to Ganesha in your music system or if you know one chant it.
Mediate for some time.
Touch the feet of the idol of Ganesha and thank him for helping in a successful puja.
Take the flowers, sandalwood or sweet or fruit and share it with those present at the puja or if you are alone you can eat a piece of it.
Note: Milk is usually used to do abhisheka or wash the murti in temples. This is avoided in home puja.
Please note that what is important in Hinduism is not the ritual but devotion. Ganesha accepts anything when it is offered with devotion.