What is a good ritual to glorify Allah (Tasbeeh) during the day? I like to keep on mentioning Allah all through the day, even while cooking, working in the house, driving and so on.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The best Dhikr (mention of Allah) at all and the best Tasbeeh is the Quran.  No doubt about that.

There are other forms of Dhikr that have great merit such as saying: ‘Laa Ilaaha Illa Allaah Wahdahu Laa Shareeka Lahu Lahul Mulku Wa Lahul Hamdu Wa Huwa ‘Ala Kulli Shayeen Qadeer’ (100 times).  It was reported that “Whoever says it (the above Dhikr) 100 times in a day, it is as if he had freed ten slaves, he gets 100 rewards and one hundred of his sins are erased, and it (this Dhikr) becomes a protection for him from Satan all that day until the evening and nobody will do anything better than what he did except someone who did more than him.”  [Reported by Al-Bukhari and Muslim]

Muslim also reported from Abu Hurayrah,  that the Prophet said: "Whoever says, when he gets up in the morning and after sunset: ‘Subhana Allaah Wabi Hamdihi’ one hundred times, nobody will do anything better than him except the one who did the same (number) or more."

Finally, we advise you to get a small book entitled: Hisn Al-Muslim (The Fortification of the Muslim).  There is an English version available in Islamic centers and libraries.

Allah knows best.