Allah sends a lot of blessings in the form of answering prayers, helping, giving peace, protecting, giving respect and a lot of other forms. So, my question is, how can we be thankful to Allah for all his blessings?
A short and simple answer is quoted in (2:152)
So remember Me; I will remember you. And be grateful to Me and do not deny Me.
Is don't deny Allah by believing in him, as deny here is the translation of "kafara" which also means disbelieve.
In fact we are encouraged to thank Allah, even if we will not be able to thank HIM the way we should as it is stated in two verses of the Quran.
Once as a supplication of the Prophet Sulayman ():
... "My Lord, enable me to be grateful for Your favor which You have bestowed upon me and upon my parents and to do righteousness of which You approve. And admit me by Your mercy into [the ranks of] Your righteous servants." (27:19)
and in another verse
..."My Lord, enable me to be grateful for Your favor which You have bestowed upon me and upon my parents and to work righteousness of which You will approve and make righteous for me my offspring. Indeed, I have repented to You, and indeed, I am of the Muslims." (46:15)
So the best way to thank Allah is by following HIS orders, and leaving anything HE has prohibited.
And by the remembrance of Allah (dhikr), so anytime call him for supplication by praising HIM by HIS beautiful names.
Here some ahadith about what some people may call the power of saying: Alhamdulillah (praise due to Allah) or allahuma lakal hamd (O our Lord to You is the praise):
One day we were praying behind the Prophet. When he raised his head from bowing, he said, "Sami`a l-lahu liman hamidah." A man behind him said, "Rabbana wa laka l-hamdu, hamdan kathiran taiyiban mubarakan fihi" (O our Lord! All the praises are for You, many good and blessed praises). When the Prophet completed the prayer, he asked, "Who has said these words?" The man replied, "I." The Prophet said, "I saw over thirty angels competing to write it first." Prophet rose (from bowing) and stood straight till all the vertebrae of his spinal column came to a natural position. (sahih al-Bukhari)
While we said prayer with the Messenger of Allah (ﷺ), one among the people said: Allah is truly Great, praise be to Allah in abundance. Glory be to Allah in the morning and the evening. The Messenger of Allah (may peace be upon, him) said: Who uttered such and such a word? A person among the people said: It is I, Messenger of Allah (who have recited these words). He (the Holy Prophet) said: It (its utterance) surprised me, for the doors of heaven were opened for It. Ibn 'Umar said: I have not abandoned them (these words) since I heard the Messenger of Allah (ﷺ) saying this. (sahih Muslim)
Note that there's also a difference between gratefulness (hamd) and thankfulness (shukr) according to most scholars while others say they are equal. See for example this fatwa islamqa#146025:
Hamd can only be expressed verbally, unlike shukr, which may be expressed verbally, in the heart or by one’s physical actions.
Hamd may or may not be in return for a favour or blessing, unlike shukr, which can only be in return for a favour or blessing.
A quote from ibn al-Qayyim from the same source:
Shukr is connected to favours but not intrinsic attributes. So it cannot be said “we thank (shukr) Allah for being Ever-Living, All-Hearing, All-Seeing, All-Knowing”, but He is to be praised (hamd) for these attributes, just as He is to be praised for His kindness and justice.
Shukr may be for kindness and favours. Everything to which shukr is connected, hamd may also be connected, but the converse is not true. Everything that may be a cause for hamd may be a cause for shukr, but the converse is not true, for shukr may be manifested in physical actions, whereas hamd is in the heart and on the lips (beliefs and words).
Only imam at-Tabari seems to set both of them equal.