Modern Science is unable to explain the process of creation as of now. The Big bang theory and Steady State theory have many loop holes and they do not appeal to everybody. Anyways, I will not discuss Modern theories of creation here. I am going to state what Vedas say about creation. Vedas are the sacred text of Hinduism, just like Bible for Christanity. Creation has many aspects, and it is not possible to talk about them in this article, so I will talk only about different phases of creation. Chapter 2.5 and 3.10 of Srimada Bhagavatam deals with the process of creation. Note that the Puranas, Upanishads are also considered as part of Vedas, besides 4 main Vedas. Before stating the theory, let me clear that English language does not have exact equivalents of the terms used in Vedic literature. So, I am using the terms and language used by other translations although the exact interpretation can be understood by reading the original text in Sanskrit, or in similar languages like Hindi. To understand them completely, please refer to Chapter 2.5 and 3.10 of Srimada Bhagavatam. From now on, I will use SB to refer Srimada Bhagavatam, and BG for Bhagavata Gita.

Here is the theory:
There are three basic material modes (qualities) of nature: mode of goodness (Sattva), mode of passion (Rajah) and mode of ignorance (Tamah). (SB 2.5.18)

There are nine phases in creation besides the one which naturally occurs due to the interaction of these three modes. In this article, we will mostly look into these nine phases. Eternal time is the primeval source of the interaction of the three modes of material nature. (SB 3.10.14, 3.10.11)

1. Of the nine creation, the first one is the creation of Mahat-tattva which is the result of incarnation of Supreme God (known as Karanarnavasayi Visnu). Then time is manifested. And in course of time, the three modes or qualities appear. Then, in the course of time, the three qualities interact resulting in further creation. (SB 2.5.22, 3.10.15). Note that time is created by Supreme God. So for him, everything (beginning, end) is occurring at the same moment.

2. Material activities are caused by Mahat-tattva’s being agitated. Thus, in the 2nd phase of creation, the false-ego (Aham) is generated in which the material ingredients, material knowledge and material activities arise. (SB 2.5.23, 3.10.15)

3. The sense perceptions and elements are created in 3rd phase of creation. Here are the details:

a. From the darkness of false ego, the first of five elements, namely the sky (nabhah), is generated. Its subtle form is the quality of sound, exactly as the seer is in relationship with the seen.
b. In the course of eternal time, due to the transformation (reactions) in the sky, the air is generated with the quality of touch, and by previous succession the air is also full of sound.
c. In the course of eternal time, due to the transformations in the air, the fire is generated, taking shape with the sense of touch and sound.
d. In the course of time, due to the transformations in the fire, the water is generated, full of juice and taste. As previously, it also has form, touch and sound.
e. In the course of time, due to the transformations in the water, the earth (solid) generated with the sense of odour. Thus, the qualities of sense perceptions are fully represented in earth.

So the transformation took place in the following order: ether (or sky) -> gas (air) -> fire -> liquid -> solid. (SB 2.5.25-29, 3.10.15, BG 10.8)

4. The fourth creation is the creation of knowledge and of working capacity. (SB 3.10.16) This can be understood as the laws of nature.

5. The 5th creation is that of controlling deities by the interaction of the mode of goodness, of which mind is the sum total. (SB 3.10.17)

6. The 6th creation is the ignorant darkness of the living entity, by which master acts as a fool. (SB 3.10.17)

Thus, after the creation of Mahat-tattva, time was manifested. Then 3 qualities of nature emerged in it. Then false ego was created. Then due to mode of ignorance, matter (5 fundamental elements) was created. Then its knowledge, and different activities of material knowledge come into play. In other words, the powers that evolve matter, the knowledge of material creations, and the intelligence that guides such materialistic activities were generated. Mind was created due to mode of goodness. Sense organs were created due to mode of passion.

When all these became assembled by force of energy of Supreme God, this universe came into being. All the above are natural creations by the “maya” of the Supreme Lord. Then a demi-god (Brahma) known as creator of the universe came into existence, who has the brain like that of Supreme Lord.

7. The 7th phase of creation is that of the immovable entities, like creepers, the trees with and without flowers, pipe plants etc. They are of 6 kinds. (SB 3.10.19)

8. The 8th phase of creation is that of lower species of life, like cow, goat, ass, mule jackal, tiger, birds etc. They are not intelligent species. (SB 3.10.21-25)

9. The 9th phase of creation is the creation of human beings. In the human race, the mode of passion is very prominent. Humans are always busy in the midst of miserable life, but they think themselves happy in all respects. (SB 3.10.26)

10. The 10th creation, which naturally occurs due to the interaction of three modes are the creation of the demigods. They are of eight varieties: (1) the demigods, (2) the forefathers, (3) the asuras, or demons, (4) the Gandharvas and Apsaras, or angels, (5) the Yaksas and Raksasas, (6) the Siddhas, Caranas and Vidyadharas, (7) the Bhutas, Pretas and Pisacas, and (8) the superhuman beings, celestial singers, etc. All are created by Brahma, the creator of the universe. (SB 3.10.28-29)

Any theory of creation is incomplete without estimating the age, shape and size of universe. Vedas say that our universe is about 155.52 trillion human years old, and its total life span is 311.04 trillion human years (which is equivalent to 100 years of Brahma). In Srimada Bhagwata 5.20.38, the diameter of the universe is quoted as 500,000,000 yojanas (1 yojanas is equal to approx 9 miles, so its 4.5 trillion miles). The shape of the universe is egg shaped (brahmanda = brahma+anda). It may be interesting to observe that distance traveled by light in one day (186,000,000 * 3600 * 24 =~ 16 trillion miles) is equal to the perimeter of (vedic) universe (approximating ellipse to circle, perimeter of universe = 4,500,000,000 * 3.1416 =~ 14 trillion miles).