Why are the sefirot not considered a problem of Shituf? Is there anything wrong with believing in sefirot?
The idea behind the Sefirot is as follows.
Therefor, the Sefiort are not shituf because they are a step away from Gd.
However!... According to many davening to the sefirot is 100% shituf. (No different than davening to Angels to ancestors) One must be careful when asking for the "unification" of Ykvk and the Shechinah, that they have in mind the idea that they are asking Gd to unifiy the two concepts and methods to have the same outcome. They are not actually davening to the emanations.
It could be argued by some, that a lack of understanding could lead one to have Shituf if they distinguish between YKVK, Elokim, etc in their davening. To put it another way, one might ask why the various names of Gd is not shituf.
Someone asked the Rivash this question. He answered that a Mekubal told him that one prays only to Hashem himself. "Asking" the sefiros is like asking a king to give you something through a channel. The Rivash answered that he would rather pray to Hashem directly and let him decide how to give him his request.
The 3rd Rebbe of Lubavitch explained in Derech Mitzvosecha and here that the sefiros are not one with Hashem's essence, they are the revelation of Hashem, and even that revelation is one, just the "vessels" change the light into different forms.
The Mitteler Rebbe of Lubavitch wrote a book called Shaar HaYichud. In this sefer the M.R. explains the entire "Seder Histalshelus" from Atzmus Ohr Ein Sof (Essence of the Light that is Infinite) to Malchus of Malchus of Asiyah.
Sefiros are methods (as stated above) for which Hashem (Ein Sof) brings the entire creation into existence. A primary source of source for Seder Histalshelus is "Chesed" (ch. 11)
Note Birkas Shema that we say "Kulam B'Chochma Asysah"
Through Hashem's names and Sefiros, creation is created Yesh M'Ayin, and it functions.
Note Birkas Shema "U'Tuvo, M'Chadesh BKol Yom Tamid Maseh Bereshis"
Kabbalah states that we channel Hashem's Hashpa in blessings we make using different sefiros. Each of the names of Hashem connects to a different Sefira.
The Blessings of Shemonah Esrei all connect to different sefiros and during prayer you are able to draw down Hashem's Hashpa through those sefiros.
With all this said, a person who does not understand this process as well as what will be said below will be worshiping something other then Hashem C"V. If it is actual Avodah Zarah would be up to debate. Shituf would only apply if you actually understand what "Chochmah" is and really believe that Chochmah has to power to create something for you. Outside of bowing to Idols, slaughtering sacrifices to them, and worshiping them in the way they are worshiped ie: Throwing rocks are Mercury" it is not avodah zarah proper to pray to sefiros since this is not their primary form of worship. Regardless it is foolishness and one of the unfortunate side effects of learning Kabbalah without a real understanding of what you are learning.
Once the blessing formula is broken down "al pi Kabbalah" it is easy to see how the process works.
Baruch - The root is נרך which means to kneel. Baruch is not just "Blessed are you" but it is a request to bring down blessing. From where?
Atah - Atah represents Atzmus Ein Sof. It is higher thatn all other names, including YKVK. We ask that Hashem (Ein Sof) draw down blessing for us. Through?
YKVH - Hashems name that connects to Tiferes which bridges Chesed and Gevurah. Its mercy. This name can be connected to different siferos for different blessings and bring down the blessing through that.
Example: Shemonah Esrei Blessing 4 "Chonen HaDoas" is connected to the level of Chochmah since we are asking Hashem to instill us with Wisdom, Understanding, and Knowledge.
One of the reasons why the Rivash rejected this approach to prayer is how it could easily result in undesirable affects.
The average Jew should focus on Pirush HaMilos (Simple meaning of the words) and not concern themselves with Sefiros.
The Alter Rebbe writes in his siddur that if one is not able to use kabbalistic kavanah during prayer he should have a general kavanah that his prayers should be heard by Hashem and lifted up with all the Kavanahs in their place.
Another way of saying the same thing as the answers above, but in a way that might be easier to understand for some lesser-initiated readers of this question:
Human beings cannot perceive G-d. We can only perceive the ways that G-d's manifests his Will into human existence.
We call the Source of G-d's Will the "Ein Sof". We can't describe G-d's essence in any positive terminology, for any description at all would itself be a false limitation. Instead, we refer to G-d at "Without End".
The lowest sefirah is malchus - kingship. That is the sefirah farthest away from Ein Sof - i.e. our physical world.
The other nine sefiros represent various manifestations of G-d's will. The closer the sefirah is to the Source, the less that human beings are capable of experiencing that manifestation of G-d's Will.
This is one of the reasons why kabbalah was never studied by the general public until very recently in Jewish history. Kabbalah uses descriptions like "closer to" and "farther from" G-d, even though G-d is not a physical entity, and therefore is never "close to" or "far from" anything.