There are different perspectives. This is an advaita perspective (the belief that all Gods are One.)
What are the three gunas
The three gunas are:
Tamas - this is the quality of laziness, darkness (ignorance) and inertia.
Sri Swami Sivananda on tamas process
Tamas is inertia or inaction or darkness.
Tamas binds man to heedlessness (Pramada), laziness (Alasya) and sleep (Nidra).
Sometimes Tamas prevails and the man becomes slothful. He feels lazy, indolent and lethargic. He is dull and feels sleepy. When Tamas prevails, Sattva and Rajas are overpowered for the time being.
Tamasic action is ignorance. Those who are established in Sattva rise upwards. The Rajasic people occupy a middle place and the Tamasic people go downwards, shrouded in the vilest of qualities.
Rajas - this is the quality of activity, energy, agitation and excitation.
Sri Swami Sivananda on raja guna
The Rajasic mind always wants new sensations and variety. It likes certain persons, objects and places now and, after some time, it becomes disgusted with them and wants new persons for company, new vegetables to eat, new books to read and new places to see (finds pleasure in sightseeing).
Sattva - this is the quality of goodness, balance, purity and peacefulness.
Sri Swami Sivananda on sattva guna
A Sattvic mind is always steady. It finds delight internally. It may stick to one place indefinitely. It keeps friendship with persons for a long, long time. It can read the Gita or the Yogavasishtha any number of days. It can live on Dal-roti for years together without any grumbling.
Who is Trimurthi
According to Advaita, the Trimurthi are not three different Gods with distinct identities, but rather they are One and the same God.
Lord Shiva by Sri Swami Sivananda
Brahma represents the creative aspect, Vishnu the preservative aspect, and Siva the destructive aspect of Paramatma. This is just like your wearing different garbs on different occasions. When you do the function of a judge, you put on one kind of dress. At home, you wear another kind of dress. When you do worship in the temple, you wear another kind of dress.
Thus Brahma is the creation aspect, Narayana is the protection aspect and Paremeshwara is the destruction aspect.
How do they map onto the three gunas?
This is the common and popular way to map the three Hindu trimurthis onto one of the gunas.
Brahma - Rajas - because creation implies activity and energy.
Narayana - Sattva - because protection or sustenance is a state of continuity or balance
Tamas - Destruction - because destruction implies death. and death is a product of tamas.
Lord Shiva by Sri Swami Sivananda
You exhibit different kinds of temperament on different occasions. Even so, the Lord does the function of creation when He is associated with Rajas and He is called Brahma. He preserves the world when He is associated with Sattva Guna, and He is called Vishnu. He destroys the world when He is associated with Tamo Guna, and He is called Siva or Rudra.
Brahma, Vishnu and Siva have been correlated to the three Avasthas or states of consciousness. During the waking state, Sattva predominates; during the dream state, Rajas predominates; and, during the deep-sleep state, Tamas predominates. Hence Vishnu, Brahma and Siva are the Murtis of Jagrat, Svapna and Sushupti states of consciousness respectively. The Turiya or the fourth state is Para Brahman. The Turiya state is immediately next to the deep sleep state. Worship of Siva will lead quickly to the attainment of the fourth state.
However I have also seen the following interpretations (I am still looking for some online/scriptural references to these. If anyone has come across this, then please comment and I will be happy to edit it)
Example 1, creation as tamas
Creation is a result of ignorance. In reality (advaitic terms), there is no creation. The perception of creation is only ignorance.
Example 2, destruction as sattva
Shiva - Sattva - here Lord Shiva is seen as the destroyer of ignorance or ego. Thus liberation or the final goal of life leads to equanimity, steadfastness, peace, bliss and unity with God. Thus in this sense Lord Shiva is seen as Sattva.
So basically it depends on how you view things. If you view creation as a positive thing, you would say that creation is sattva. If you view destruction as a positive thing you would say destruction is sattva. If you view protection as a positive thing you would say protection is sattva.
The reality (in terms of advaita) - God is beyond all Gunas
God or Brahman is above and beyond all gunas. He is nirguna and nirakara. These gunas are simply ways in which we have interpreted the Lord. But the Lord Himself is unattached and beyond the gunas.
Bhagavad Gita 7.13
tribhir guṇa-mayair bhāvair
ebhiḥ sarvam idaḿ jagat
mām ebhyaḥ param avyayam
Deluded by the three modes [goodness, passion and ignorance], the whole world does not know Me, who am above the modes and inexhaustible.
All the best.