Read
Mortalium Animos by Pius XI and
Humani Generis by Pius XII. Also read
"An instruction of the Ecumenical movement" by Pius XII.
Pretty much, we are to pray and encourage others to convert to the One True Catholic Church outside of which no one can be saved.
The above is the difinitive answer… however it leaves out the Human element and methods of witness.
Ecumenical dialogue and inter-church co-operation can be very positive, and usefull.
Actions which foster sectarian tensions are very dangerous and give extra weight to those in our society who claim that Religion is a cause for tensions and wars.
Getting involved in activities with people of other faiths provides opportunities to build understanding, be seen to be able to get along (which helps reduce fears in the whole community… especially when that co-operation is visible) and can help create situations where people of different sects of christianity or entirely different faiths can co-operate on important areas where we have common moral ground.
An example would be in fighting the current trend in many countries towards major legal limitations being placed on traditional religious freedoms. By working together we can all stand up and be counted together in saying that no government has the right to restrict practice of or membership of any legitimate religion.
We can work closely with many other christians on areas of common moral understanding such as Pro-Life issues, and definition of marriage We can also work with people of other faiths such as the Muslims on similar areas.
We should also stand up for the religious freedoms of other faiths even when the issues at hand do not directly impinge on the normal practice of average catholics: an example would be the banning of traditional head scarves in public. Such laws are often targeted at Muslim women, but they have the right to dress this way. They have the right to express their faith and culture in a visible way.
Making such a law would also discriminate against some traditional Catholics such as some of the more traditional orders of nuns who still wear a full veil. (or have returned to wearing one)
Some (though not very many) catholic women in the laity, as well as members of some sects such as the Amish and their similar Bretheren also prefer to wear head scarves and can be caught by these laws.
Ecumenical movements can also provide a more explicitly evangilical environment to share the truth. Bible studies or “Circle” groups held by a wide range of Lay Ecclesial Organisations (and a Personal Prelature), are often ecumenical in nature, opening their doors to non Catholics. When done properly these groups should take care to ensure that where differences in theology or biblical interpretation exist that the Catholic position is carefully explained. By defending our faith to non Catholics we become much more familiar with it and confident in it. In these environments it should be the aim to expalin our position but not require or expect the non catholic attendants to automatically accept our position or to convert.
Care does need to be taken that such meetings or groups do not deteriorate into recruiting grounds for other denominations, but that proper catholic apologetics is put forward.
Tue conversion is always the result of the work of the Holy Spirit, and most often as a result of the personal witness of people who let the world “Know they are Christians by their Love.”