You do not need to be Catholic in order to come to Mass. By all means, come! If you do not know when to stand, sit, and kneel -- don't worry about it, that is a small matter and one that will come with time. But visitors, especially ones who may not be Catholic, or even Catholics and parishioners themselves, may wonder if they can receive Holy Communion. It is a good, considerate, and thoughtful question. The question will be taken up here but if you need somewhere to check when you come, the Pew Missal is used at all 3 of the parishes and the inside of the back cover provides the guidelines for reception of Holy Communion.
For Catholics: those who have been baptized, have made their First Communion, and are in a state of grace -- that is to say who are not conscious of any unconfessed mortal sin -- may receive Holy Communion. Two common mortal sins today are: 1) missing Mass on a Sunday or Holy Day through one's own fault or choice; and 2) any use of sexuality outside of a valid marriage. These are by no means the only mortal sins, only (perhaps) the most common ones today. Mortal sin is called mortal because it completely breaks our relation with God. Thus, if a Catholic is aware of a mortal sin that they have not yet taken to Confession, then they need to bring that to Confession before returning to Holy Communion.
For Non-Catholics: Only those who have been received fully into the Catholic faith may receive Holy Communion, which means that baptized non-Catholics would need to be first received fully into the Church, and profess the Catholic faith, before receiving Holy Communion (if that is something you are interested in, go to the 'Becoming Catholic' page under the Liturgy tab). Of course a person might wonder why that is? Marriage is a good analogy. When a man and woman enter into a valid marriage, they are giving a full yes to each other but in doing so, they are saying no to all others; they are saying: to you and you alone do I enter into this particular love relationship. They will love others but this particular love relationship is exclusive to them alone. Marriage is a reflection of the nature of the relation that God wills to enter into with man and thus also the nature of our relationship with His Church -- the Mystical Body of Christ, with Christ as the head. The nature of that relation is also meant to be full and exclusive, forsaking all others. We are first joined to that Church with a profession of faith (like vows in a marriage), forsaking all others and then that relation is consummated with Holy Communion.
When a Catholic comes to Communion, the priest raises the consecrated host, the person of Jesus, and says: the Body of Christ. The person receiving Communion responds: Amen. The Amen means: I believe. But that Amen is much more than a simple acknowledgement of belief that this is truly the Body, Blood, Soul, and Divinity of Christ, the person of Jesus. It is like the vow of marriage. It says: yes I give myself fully to you and only to you, exclusively to you (to your Mystical Body the Church), forsaking all others. It is an Amen not to just one article of the faith but to all that God has revealed and teaches in and through His One, Holy, Catholic, and Apostolic Church, it is an Amen to His Church.
The Church has no desire to exclude anyone from Communion, in fact the exact opposite is true. The Church, following our Lord, wants everyone to come into full Communion with His one Mystical Body, the Church, with Him as the head. It is simply a falsehood to claim otherwise. The Lord gave His Church the responsibility for guiding everyone to this full communion. The Church has no alternative but to follow our Lord and His will faithfully; it is not a right as much as it is a God-given duty. Should we betray Him because someone demands that we do? Was this not the way of Judas Iscariot and even Lucifer himself? Is this the kind of Church you want to be part of, one that readily tosses aside the Divine Will in favor of human will?
One thing to guard against, especially today -- Catholics and non-Catholics alike -- is a sense of entitlement, a form of pride that has become very prevalent; an entitlement that says I should get whatever I want and no one has a right (or duty) to set terms for me, not even in your own house! Humility is the most fundamental of all the virtues; we cannot have any other virtue, not even a living faith, without it. You can barely turn a page of Scripture without at least some implicit condemnation of pride and an exhortation to humility. Which is humble, to say: 1) yes Lord, you set the terms, or: 2) No, God or whoever you are, I set the terms? And how can real humility be lived out if there is not a real authority, a prophet (one who speaks on behalf of God, under the guidance and inspiration of God), here on earth to tell us those terms? If it is simply me who decides the terms, then we are back to #2, the way of Judas, the way of Lucifer. He did give us an authority, a prophet, and it is the Catholic Church. Do not be afraid of this. It is good, even necessary, to have a guide and a protector.