Shankaracharya has depicted the forms of Lord Ganesha very beautifully. If you read the Ganesha Atharvashisha (Upanishad), you will know of many forms of Lord Ganesha. Ganesha is present in all directions, in every possible form - the Earth, Air, Sun, Moon, in every form of nature. You are Brahma, Indra, Shiva, Rudra etc., they are all in your form. You can see the form of paramatma (Supreme Being) in one God, the formless in one form - this is known as meditation.
We recite the Ganesha Stotram –Shuklam Baradaram Vishnum, Shashivarnam Chaturbhujam, Prasanna Vadanam Dhyaayeth, Sarva Vighno Pashantaye. This does not have the name of Ganesha at all!
Shuklam Baradharam means the one who is dressed in white, the one who is pure. Vishnum means that he is at the very core of our being.
Shashivarnam means milky white like the full moon, cool like the moon that soothes us, and it has the rays of brightness. (There are two types of brightness, one like the sun that can hurt our eyes, and the other is so soothing that we can keep on looking at it.) Chaturbhujam, bhuja means shoulders that can bear weight, while chatur means cleverness or intelligence, which together means - one who can bear the burden easily.
Prasanna vadhanam dhayeth means that if you meditate on the one whose face is so peaceful, pleasant and remember them, you feel instantly uplifted. Sarva vighno pashantaye, then that one will give you the strength in the mind to overcome all obstacles.
This is not just for Ganesha, it is also related to Vigneshwara, but the most important part in this shloka is about the One who is present everywhere.
If you think God is angry with you, if you feel that you have committed a mistake and feel distant from him; or if you feel that God is always happy and content with you, then you develop a relationship with him.
Many times people say that you are angry with us, as if I don’t have any other work. You make a mistake and I get angry! Why should I get irritated if you make a mistake? Why will a Guru get angry? A Guru is always happy. I feel compassion if you make a mistake.
I feel, "Oh my God, why is he putting himself through so much hardship?" That is why if you think of something pleasant, remember a pleasant face, you get strength! When we think of something pleasant in our mind, the fear of the unknown goes away, we get strength to overcome the obstacle.
What is the form of Ganesha? Ajam nirvikalpam means someone who was not born. Nirakaram ekam - you have no form, you are the only one, and there is no one else. Nirananda mananda madhvaita poornam - you are happiness. you are the only one, the whole world is in your form.
The shloka continues with Param nirgunam nirvisesham niriham para brahma roopam ganesham bhajemam, you are the form of the parabrahma, you are present everywhere, you have the chaitanya shakti, the scintillating energy, I meditate on you in my mind.