I am a Methodist currently dating a girl who is Catholic. How does the Church feel about Catholics marrying non-Catholics, and what would we have to do? (Also, I am not very attached to the Methodist faith.)
Mixed marriages are discouraged because they inevitably involve pain for the spouses (the only time they don’t is if neither spouse cares about his or her religion), and they set a bad example for the children because the parents are not united in the most important area of life—their relationship to God. This can lead to confusion, weak faith, and even lost faith on the part of the children.
Although mixed marriages are not recommended, the Church grants dispensations for Catholics to marry non-Catholics. To see about obtaining one you should see a parish priest.
If you are thinking seriously about marriage, I would urge you to investigate the Catholic faith and consider becoming a Catholic. It is far better on a human level if the spouses are religiously united. It is better both for children they have and for them, not only in that it prevents conflict but also in that it allows them to share true spiritual intimacy, which they otherwise are blocked from having.