How does one go to Confession before receiving the Eucharist if I am not Catholic?

As part of your adult initiation and before you become a member of the flock you make confession. Now if you are unbaptized and will be baptized at Easter in the Church, that will wipe all sins up to that point away. This source does not appear to answer the question, but I will put it down until I can find another one. Rite of Christian Initiation of Adults

Catholic sacraments are for Catholics.

Catholic sacraments are for Catholics and Catholics are to receive the sacraments from Catholic ministers.

Can. 844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of §§2, 3, and 4 of this canon, and ⇒ can. 861, §2. - Immensae Caritatis

However, there are circumstances when non-Catholics may receive Communion from a Catholic priest. This is especially the case when it comes to Eastern Orthodox Christians, who share the same faith concerning the nature of the sacraments:

"Catholic ministers may licitly administer the sacraments of penance, Eucharist and anointing of the sick to members of the oriental churches which do not have full Communion with the Catholic Church, if they ask on their own for the sacraments and are properly disposed. This holds also for members of other churches, which in the judgment of the Apostolic See are in the same condition as the oriental churches as far as these sacraments are concerned" (CIC 844 § 3).

In your particular case, you must take an RCIA course in order to be instructed on what the Catholic Church teaches and believes. Once an individual is ready to make a Profession of Faith into the Church, one will normally make a confession the day before he makes his public Profession of Faith and receives the Eucharist. This is the practice in my archdiocese.

That said one should be aware that Non-Catholics may go to confession under very limited circumstances.

Can. 844 covers exceptional circumstances when Catholics can receive the sacraments of Penance, Eucharist, and Anointing of the Sick from non-Catholic (but validly ordained) priests, as well as those exceptional circumstances when non-Catholics can receive those three sacraments in the Catholic Church.

Note well the important word “exceptional”.

Can. 844, states in paragraph 4:

“If there is a danger of death or if, in the judgment of the diocesan bishop or of the Bishops’ Conference, there is some other grave and pressing need, Catholic ministers may lawfully administer these same sacraments to other Christians not in full communion with the Catholic Church who cannot approach a minister of their own community and who spontaneously ask for them, provided that they demonstrate the Catholic faith in respect of these sacraments and are properly disposed.”

First situation: danger of death. Here the priest makes the determination. If a priest approaches a car accident where a man is dying and the priest asks if he can be of any assistance, and the man says, “Father, I’m a Lutheran, but I know I’m dying and I want to meet my Lord with a clear conscience. Could you hear my confession?” The priest could determine that, yes, the conditions warrant him hearing the confession of this Lutheran.

Next: outside the danger of death. Notice who makes the determination: not the priest, but either the diocesan bishop, or the whole Bishops’ Conference. If there were a general persecution of Norwegian Lutherans in my native Minnesota, and all their ministers were being rounded up and sent to the state pen in Stillwater or St. Cloud, the diocesan bishops could determine that this exceptional situation warrants exceptional action. He could permit his priests to absolve, communicate, and anoint Norwegian Lutherans who come to them, provided these Lutherans “demonstrate the Catholic faith in respect of these sacraments.”

Bottom line: in situations where there is not danger of death, it is not up to us – even to the priest – to determine if the conditions are met for these exceptional cases. The bishop decides! If there is time to consult the bishop, consult the bishop! - Can non-Catholics go to confession?

That said, in the meantime one can and should make a perfect act of contrition.