APPEASEMENT OF THE SAGES

Any serious enough and sustained enough effort at contacting the spirits of Gensokyo will most likely draw in the attention of the Sages.
I was in some kind of contact with other kami from Gensokyo for perhaps 3 weeks before Okina-sama made herself known to me.
Besides Okina-sama, the known Sages are Yukari-sama and Kasen-sama.
Which of them come for you depends on the circumstances and what kind of person you are.
They have many roles, but an important one is to act as gatekeepers.
This prayer and ritual is meant to appease them so that you will not have problems with them.
My personal experience is that they will not hassle you if you are respectful and have no ill intentions towards the denizens of Gensokyo.
Beyond acting as a "border control", they can of course facilitate access and are incredibly powerful allies to have.

You should have an offering of incense, sweets (dango is preferable), water, rice and alcohol (sake is preferable).
Any attempt to directly invoke any of these beings should be done with utmost deliberation and caution, but as this a simple prayer I think any excessive protection measures might just be viewed with suspicion.
It gives the vibe of walking into a small town and asking the elder if you can speak with the locals while you are holding a gun.

If for some reason you happen to feel their presence very strongly, don't panic.
The Sages are all very powerful entities.
Their presence can be overwhelming even if they would have completely bening intentions.
Acknowledge them and ask what they would like to communicate.
If they feel clearly hostile (I assure you, hostile spirit entities will make it known) you should apologize and beg for mercy.
I find any kind of immediate or severe hostile reaction unlikely, but I can't say it won't ever happen.
Do not do this or anything else with impure motives.

You should do this daily for a week at minimum. Ideal would be from full moon to full moon.
Solar eclipses and solar storms are auspicious.
If you feel very clearly that you have been answered, you don't need to do this any further.
It might be a good idea to pay tribute to the sages from time to time nevertheless.

The prayer

(Face towards where Japan would be from your POV. If you are in Japan, face towards Nagano.)
(Bow deep twice)
(Clap twice)
(Put your hands together, one thumb over the other)

I CALL YOU
AND ONLY YOU
SAGES OF GENSOKYO
WHOSE NAMES I SHOULD DREAD

(Repeat above in sequence of fours untill you feel a change in your consciousness)

I CALL YOU
SAGES OF GENSOKYO
SEEN AND UNSEEN
KNOWN AND UNKNOWN

I CALL YOU
TO MAKE AN OFFERING
TO LET YOU KNOW
THAT I COME IN PEACE

(make the offering)

YOU HIDDEN AND RADIANT
MIGHTY AND POWERFUL
YOU WHO GOVERN
THE LAND OF ILLUSIONS

YOU WHO REMAIN UNSEEN
YOU WHO CONTROL BOUNDARIES
YOU WHO GUARD THE GATES
AND YOU WHO OPEN THE DOORS

I HAVE STARTED TO SEE
WHAT WAS ONCE UNSEEN
AND I DESIRE TO HONOR
THE SPIRITS OF GENSOKYO

TAKE MY RESPECT!
TAKE MY ADORATION!
SO I MAY GIVE IT
TO OTHERS TOO!

PLEASE TAKE MY HUMBLE OFFERING
GIVEN WITH A HONEST HEART
PLEASE TAKE MY HUMBLE OFFERING
GIVEN WITH PURE INTENTIONS!

(Your heart better be honest and intentions pure..!)

LET ME ADORE THE MYSTERY
THAT I WOULD NEVER CRUDELY PEEL
LET ME WITNESS MARVELS
FROM REALMS OF FANTASY

(Bow)

THIS I MOST HUMBLY ASK OF YOU!