Worshipping Lord Surya can be done
in many ways, but here's a standard, but precise, way, which you can follow,
specially meant to suit the present day busy life schedules:
Materials
Needed

Idol / Picture of the Surya (Sun God)
(optional, because the shastras, or some contexts, say,
Surya is swayamprakashita, i.e. self-revealed form of the Supreme.)
Table, bench or box
Two metal vessels
Uddharana or metal spoon
Pieces of clean cloth (preferably red) to put on the altar
A piece of clean string (symbolic yagnopaveet)
Kumkum, Turmeric (haldi) and cups to hold them
Akshata (uncooked yellow rice) in a cup

Sandal paste
Incense Sticks
Camphor
Fresh (red) flowers (preferably javaa, i.e. hibiscus/chona rose), Bel
leaves
Fruits, Coconut, fruit juice
Naivedyam (food offering)
Lamps with wicks soaking in oil or ghee
Aarati plate with oil soaked wicks
(N.B.: Lamps and aarati plate
are optional because the shastras, or some texts, say, Surya is the
source of all lights and fire, so lightening him up with a physical lamp is
immaterial, or according to other texts, Surya is offended when fire is shown
to Him for aarati so even if you light up lamps, don't make the flames
face the east).
Preparation
First and foremost begin with cleansing,
i.e. clean the area where the altar is to be set up. This should face the eastern
direction if possible. You and others who will participate in the performance
of the Puja should bathe, and wear clean and comfortable clothes. Men may wear
kurta/pajama combination, or dhoti/uttareeyam combination with or without a
kurta/shirt/jibba etc. If men wearing dhoti decide to wear no upper garment,
then a yagnopavita should be worn.
Altar
Set Up

A small bench or a wooden table or a
cardboard box covering an area no larger than 36" x 24" and about
15" to 24" tall is adequate. The size can vary if you wish to arrange
more or fewer pictures and/or statues on the surface. Remember that you should
be able to see the items on the altar and have easy access to make offerings
during the worship. Place the table (or box) against a wall, cover it with a
clean cloth, preferably white, and secure the same by tucking it under so that
it won't slip off easily. Tape it if necessary such that the tape is not visible.
Prayers to Lord Ganesha
Before starting the puja proper, it is
essential to contemplate Lord Ganesha (God of obstacles) to assure ourselves
that no obstacles interfere with a smooth performance of the puja rituals. Thus,
with folded hands chant the following:
Karishyamaanasya karmanaha nirvigghnena
Parisamaaptyarttham
Aadhou mahaaganapati smaranam karishye
So that the ceremonies we are about to
undertake proceed to completion without any obstacles, we contemplate on Mahaganapati.

Similarly the grihadevata, i.e.
the family Godhead, needs to be invoked as He/She is ever present bestowing
protection to the family at all times. Chant as follows:
Gruha devataam ddhyayaami Ddhyaanam
samarpayaami
I respectfully contemplate our family
Godhead.
Shuddhi
(Cleaning)
In order to assure ourselves that any
and all evil tendencies are removed from the worship room, we start with a prayer
to Shiva whose very invocation is believed to clear out any troubling vibrations.
Om namah pranavaarththaaya
shuddha jnaanaika moorthaye
nirmalaaya prashaanthaaya
dakshinaa moorthaye namaha
I salute the Lord of the Southern direction
who is the very embodiment of the sacred symbol Om and of pure knowledge and
eternal peace.
Prayer
javaakusuma samkaasham
kaashyapeyam mahaddhyutim
dhwantaarim sarvapaapagghnam
pranatohasmi divaakaram
I salute Divaakara who shines like the
hibiscus blossom, is descendent of sage Kaashyapa, of great splendor, and the
destroyer of all sins.
Upachaaraas
(offering the ingredients of the puja)

Now we are ready to invoke the Sun God
and offer Upachaaraas (reception with reverence). With folded hands, focus on
the picture of the deity as you chant the following:
Om Sri Sooryanaaraayana swamine
namaha
Om I salute the Sun God, in the form
of Lord Narayana (Vishnu), the protector and sustainer of the universe.
Now offer a few grains of akshata with
your right hand such that the grains fall on the picture gently as you chant:
Om Sri Sooryanaaraayana swamine
namaha aavaahanam samarpayaami
I offer an invocation to you offer akshata
as before such that the grains fall on the altar as you chant:
Om Sri Sooryanaaraayana swamine
namaha aasanam samarpayaami
I offer a seat to you.
Pradakshina (circumambulation)

Now stand up and do a pradakshina (circumambulation)
turning three times in a circle to your right.
Om Sri Sooryanaaraayana swamine namaha
yaanikaanicha paapaani janmaanthara
krithaani cha
thaani thaani vinashyanthi pradakshinam pade pade
Whatever sins I have committed in all
my lives May all of them be absolved as I circumambulate in thy worship.