How can I raise my adopted child so that I give Hashem a Jew?

Raising a child to be a Torah observant Jew is the same whether the child is adopted or not. Just remember that a child born Jewish doesn't have to choose that identity, and an adopted child does. Also, if a Jewish child does not choose to live a Torah life, there is always a chance for return. If an adopted child does not choose to live as a Jew, he may become negative about Jews.
Adoption of a child is a subject all to itself, but I will share my experience. When my child was handed over to me, I had heard that her mother stated her religion as Catholic and Jewish. Of necessity, we had to investigate if in fact she was a Jewish woman or not. As it turned out, she was not. So the next issue was that of conversion. My family was Orthodox, so there was no question of any other kind of conversion. We found an Orthodox rabbi and in the presence of his bais din ( rabbinical court of three men) my daughter underwent a child conversion. She was immersed in a mikveh (ritual bath) and pronounced Jewish.
The status of my daughter’s conversion worked for her until she was thirteen. At that time, we moved to another state and we sought to enroll her in a yeshiva. There she might have attended had her conversion not been at issue. It was not acceptable to the head of the school. We found another yeshiva that agreed to take her, and in the course of that year, we found another rabbi, and with his bais din, my daughter underwent an adult conversion.
But these conversions are not what made her a religious Jew, and going to a Jewish day school or Hebrew Academy as so many of these schools are called is no guarantee that a child will grow up to be a Jew and marry another Jew. I had gone to a Hebrew day school as a child, and some of my friends left the fold and married non Jews. Others did not marry at all. The education guaranteed nothing. If you want your child to become a Jew, then make that the priority in raising your child. Ask observant mothers what they give their children to listen to and to read. There are videos for the children, too.
In the early years, the child should have plenty of experiences of being Jewish. He or she should hear Jewish music and Jewish stories. There are many choices today with all the albums and literature available for the child age two to six. By the time a child enters kindergarten and first grade, he should know some of the songs related to the parshiyos (weekly Torah readings) and the stories from the Torah about the forefathers and foremothers and their lives in the early world. Children also must have good experiences of Shabbos with the family and with other families and friends.
Many people send their children to a Hebrew Day school or to what are more “modern” day schools because they want the great secular education that these schools promise. These schools may not seem to downplay the Torah portion of their curriculum, but it comes across to the children. The other problem is that the presentation of Judaism in such schools is not fun for the child and may put him off to his Jewish identity and to Torah as sometimes happens. There is no better yeshiva education for a girl than a Bais Yakov school. These schools have opportunities for the girls to experience Torah Judaism as they learn about Judaism and Jewish history and as they develop their talents, skills and character. They become models themselves of Torah Jews. As for the boys, I cannot say what there is, because I never had a son, but there are many yeshivas, and it is up to parents to observe at these schools carefully before choosing one for their sons. Bais Yakov schools provide an excellent secular education for their girls, and there is no excuse for yeshivas for boys not to do the same.
Schools and summer camps are important for a child and the right camps are crucial for giving the child an experience of Judaism with hundreds of other children that he/she would not get at the regular school. And these camp experiences help the child meet and make friends and develop relationships that will last for the rest of their lives.
At the core of raising a child to be a Torah observant Jew is that we take our Judaism and our Torah seriously. Don’t leave it up to the school or the synagogue to any of the work for you. It is up to you to do it. Keeping kosher and keeping shabbos and tzniyus (the laws of modesty) are good examples. You cannot eat out if you keep kosher unless you eat at a kosher restaurant. You cannot go to movies on shabbos if you keep the day holy. And you cannot follow the current styles of clothes if you are going to dress as an example of a modest person. And if you take the Torah seriously, then you must learn at home weekly if not daily and share what you learn with your child. Maybe you study a halachah (law) a week or you read the weekly Torah portion and share the commentaries with your child. As long as there is a modeling of the importance and validity of Judaism, you teach the child its importance.
Many people fail to impart to their children that the Torah is the essence of our Jewish identity and way of life and that its precepts are kept for good reasons, the main one being that Hashem gave the mitzvos to us men and women as they are. Too many parents do what they want to do as opposed to what the Torah says to do. They do not pray or bless their children, do not do all the rituals with their children, and they may follow a style of dress that may even embarrass their children. The women may not light the shabbos candles on time. They may never bake their own challas. They may not keep taharas mishpochoh. And they may adapt Judaism to suit themselves, in essence creating a new religion where women act like men, wearing tallis and kippah and taking aliyas on the bimah that the men are supposed to have. These behaviors make a mockery of Torah. Keep a woman’s mitzvos and leave the men to do what is given to them to do. This is so important. I have a cousin who is Orthodox. She doesn’t cover her hair and did all this egalitarian stuff. Her daughter never married and is not at all interested in Orthodox or Conservative or any Judaism. And my cousin who questioned the way I raised my daughter cries to me, “Where is my nachas?”