It can be rather difficult. A prospective bride and groom have to go through an awful lot to be married in the Roman Catholic church. Since the church regards marriage as a sacrament as well as a legal status, it may be difficult to receive it at all.
First, there is the whole matter of how Catholic you are, exactly. I have found that many people around my age (early twenties, for those of you) have been raised Catholic, but rejected a good deal of whatever they were taught. They may be doubtful about the relevance of the church to their lives in a general way, or they may have rebelled and refused to be confirmed as soon as they knew what that sacrament meant (as in my case). If either or both prospective spouse is doubtful about the validity of religion to their married life, yet they still want to get married in the church, there is a problem, as we shall see in greater detail in a minute.
Even for serious Catholics, getting married takes a lot of complicated steps. Besides the regular license required by state governments, they have to take classes to see if they are ready for the sacrament of marriage. Now, if you were brought up in a strict Catholic household, chances are you've been through a series of classes, workshops, and retreats during the course of your church-related life. You went to CCD and starvation awareness weekend and mass every Sunday, so it's not like you aren't used to talking about your religious views, or at least what a Catholic's views should be. But marriage classes are a little different. I personally have not gone through these, being neither married nor engaged, but they seem awfully difficult to me. What you and your significant other do is go through a series of interviews with a single priest. The priest will counsel you and ask you lots of questions to determine whether you are ready to get married. This means, in short, that the priest gets to decide whether the Catholic church condones your marriage. If he decides it does not, you cannot currently receive the sacrament of holy matrimony in the Catholic church.
So. This then is an especially big problem for unconfirmed people or people of another religion who want to marry a Catholic. Let's say, for instance, that I wanted to marry my current significant other, who is half Presbyterian and half Jewish. So far, so good--this could be accepted if we demonstrate enough devotion and seriousness, and if we agree to raise any kids in the Catholic church. (I'm serious, here--this is a requirement for any Catholic wishing to marry a non-Catholic in a Catholic service, as you might notice below. My parents had to agree to it.) This makes sense--you need special permission to receive Catholic sacraments if you aren't a Catholic. However, although I was raised very Catholic indeed, I am not confirmed, and am unwilling to go through RCIA in order to get confirmed. The combination of these two pretty much guarantees that we would be rejected, since I'm an apostate and am currently going to hell.
Big problem.
It does make sense, to an extent. The Catholic church is concerned about the congregation and the community of faith as a whole, so it seems fair that they would not want anyone to just get married within the church for the hell of it. But Catholicism has become not only a religious category, but a secular, cultural one as well. What then might one do, if they were a part of the more secular community? What would you do?
The Catholic catechism has a handy section on mixed marriage to which I cannot do justice, and so here it is.
Mixed marriages and disparity of cult
1633 In many countries the situation of a mixed marriage (marriage between a Catholic and a baptized non-Catholic) often arises. It requires particular attention on the part of couples and their pastors. A case of marriage with disparity of cult (between a Catholic and a nonbaptized person) requires even greater circumspection.
1634 Difference of confession between the spouses does not constitute an insurmountable obstacle for marriage, when they succeed in placing in common what they have received from their respective communities, and learn from each other the way in which each lives in fidelity to Christ. But the difficulties of mixed marriages must not be underestimated. They arise from the fact that the separation of Christians has not yet been overcome. The spouses risk experiencing the tragedy of Christian disunity even in the heart of their own home. Disparity of cult can further aggravate these difficulties. Differences about faith and the very notion of marriage, but also different religious mentalities, can become sources of tension in marriage, especially as regards the education of children. The temptation to religious indifference can then arise.
1635 According to the law in force in the Latin Church, a mixed marriage needs for liceity the express permission of ecclesiastical authority.135 In case of disparity of cult an express dispensation from this impediment is required for the validity of the marriage.136 This permission or dispensation presupposes that both parties know and do not exclude the essential ends and properties of marriage; and furthermore that the Catholic party confirms the obligations, which have been made known to the non-Catholic party, of preserving his or her own faith and ensuring the baptism and education of the children in the Catholic Church.137
1636 Through ecumenical dialogue Christian communities in many regions have been able to put into effect a common pastoral practice for mixed marriages. Its task is to help such couples live out their particular situation in the light of faith, overcome the tensions between the couple's obligations to each other and towards their ecclesial communities, and encourage the flowering of what is common to them in faith and respect for what separates them.
1637 In marriages with disparity of cult the Catholic spouse has a particular task: "For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband."138 It is a great joy for the Christian spouse and for the Church if this "consecration" should lead to the free conversion of the other spouse to the Christian faith.139 Sincere married love, the humble and patient practice of the family virtues, and perseverance in prayer can prepare the non-believing spouse to accept the grace of conversion.
135 Cf. CIC, can. 1124.
136 Cf. CIC, can. 1086.
137 Cf. CIC, can. 1125.
138 1 Cor 7:14.
139 Cf. 1 Cor 7:16.
I don't know if I am horrified or unsurprised.
Source: http://www.vatican.va/archive/catechism/p2s2c3a7.htm