How does the Catholic Magisterium advise the married laity to defend the institution of marriage? Does the Catholic Church have any practical advice for its adherents on ways to exemplify the ideal she sets of marriage between one man and one woman? 

Barring any specific discussion of same-sex relationships, what does the Church want us married folks to do as witnesses of Christ's love?
The Magisterium has offered a number of guidelines for how to live the institution of marriage, so as to make it truly life-giving, and indeed a source holiness for married couples. The best “defence” of marriage is the witness of couples who have lived out their vocation in accord with God’s plan for them.

The universal call to holiness

The Church’s recent Magisterium (since Vatican II) has emphasized that all people are called to holiness, not only those who have been called a clerical or consecrated vocation:


  Thus it is evident to everyone, that all the faithful of Christ of whatever rank or status, are called to the fullness of the Christian life and to the perfection of charity; by this holiness as such a more human manner of living is promoted in this earthly society (Lumen Gentium 40).


Married couples are no exception: the Sacrament of Matrimony is their particular path to holiness:


  Furthermore, married couples and Christian parents should follow their own proper path (to holiness) by faithful love. They should sustain one another in grace throughout the entire length of their lives. They should embue their offspring, lovingly welcomed as God’s gift, with Christian doctrine and the evangelical virtues (Lumen Gentium 41)


In other words, the grace received in matrimony is the source of their holiness, and it is fundamentally that grace, and the holiness produced by that grace—not something particular that the couples need to do—that will provide the witness that the Church asks.

The fundamentals in holiness of life

The principle “task” of married couples, therefore, is to live holy lives, and in order to do that, couples must first of all place no obstacle to living holy lives: they must, in other words, obey what the natural law tells them is necessary for a happy marriage.

First of all, the fundamental characteristics of marriage must be respected: marriage is by nature indissoluble (it cannot be ended at the discretion of the spouses), exclusive (it can only be with one spouse at a time), faithful (one cannot permit extramarital affairs), and fruitful (children are always to be welcomed). (See Familiaris Consortio, Part 3, chapter I.)

It must be specified nowadays that true marriage can only be contracted between one man and one woman, always considering the sex that they have “originally” had since birth.

The controversy over who is elegible for marriage is only one of the challenges to marriage today. There is also the relative ease with which couples can obtain civil divorce—which can easily lead couples to think that marriage is inherently transitory, not permanent—and the strong temptation to use contraception as a means to limit childbirth.

(We should note that the Catholic Church does not prohibit limiting childbirth for legitimate reasons; she merely says that actions that destroy or forcibly impede our bodies’ ability to procreate—e.g., using hormonal contraceptives or condoms, and obtaining tubal ligations or vasectomies—is immoral, because it tends to undermine both the unity of the spouses and, evidently, their God-given call to bring forth children. See Humanae Vitae, especially numbers 14-15. It is also worth noting that modern gynecology provides excellent and highly reliable alternatives to oral contraceptives, when regulating birth is necessary. See, for example, http://www.creightonmodel.com/.)

It is also important for couples to realize that they are making a very serious and permanent commitment to one another. Even if something should go wrong—either through illness, or even when one spouse is not faithful—the couple have an obligation to regard themselves as married. Separation and civil divorce can be tolerated when the situation warrants it (and when there is grave danger to one of the spouses or to the children, it might even be obligatory); however, “remarriage” is never a legitimate option, unless there is a way to prove in the external forum that the first marriage was, in fact, not a marriage at all. (See Familiaris Consortio 83.)

The first and most fundamental step, therefore, to being faithful witnesses to married love is to follow the Commandments and the natural law regarding matrimony. Nowadays, simply being faithful to the basics of morality constitutes a heroic witness, and for this a married couple can count on the grace that they receive in the Sacrament of Matrimony.

How to grow in holiness

Living a happly and faithful marriage, however, does not reduce to fulfilling the minimum requirements.

Part Three of Familiaris Consortio gives a number of suggestions in which couples can grow in holiness. Among others, 


Married couples participate in a unique way in the creative power of God. The Church encourages couples to take part generously in the gift that God has given them to bring new human beings into the world. It is a common misconception that the Church wants couples to have as many children as physically possible. That is not the case: rather, they should take into account their means and abilities. However, the Church does encourage couples—without obliging them—to be generous, not miserly, since such generosity will bring about happiness and fulfillment. (See Familiaris Consortio 28.)
Married couples have an invaluable role in educating their children. In fact, parents (not the state) are the primary educators of their children, and the institutions that exist for that purpose are meant to be at the service of parents. (Schools and governments that usurp parents’ rights to educate their children, especially as regards sensitive matters such as sexuality, commit a most grave injustice.) It is, moreover, parents who first bring their children in contact with the Church and the Sacraments. (See Familiaris Consortio 36-40.)
Strong, stable families are the bedrock of society. Espcially since there is so much upheaval today, Catholic couples are called to be examples of fidelity, and thus offset some of the ills that plague society today. (See Familiaris Consortio 44.)
The family is an image of the Church (See Eph. 5:32), and moreover, the Church’s efforts to evangelize begin with the family. (See Familiaris Consortio 50 and 52.) For example, family members can help each other to come to the Faith, or to a fuller practice of the Faith, and some familes may even feel called to dedicate themselves full time to missionary apostolate, although this will not, of course, be the norm for most families. (See Familiaris Consortio 50 and 54.) 
The Sacrament of Matrimony finds its fulfillment in prayer and the Sacraments, particularly in the Eucharist. Families draw their strength from prayer and participation in the liturgy. (See Familiaris Consortio 56-62.)


TL;DR

All Catholics are called to live holy lives, and married persons will find the source of that holiness in the Sacrament of Matrimony. In order not to place an obstacle to that holiness, at the least they need to obey what the natural law tells us about marriage: in particular, that it is the union of one man and one woman, that it is indissoluble and exclusive, that it entails fidelity, and that it must be open to procreation. This is, as it were, the minimum requirement for a happy and fulfilling marriage. Just living marriage faithfully is a powerful and even heroic witness. This, together with actively participating in the life of the Church as a family, constitutes the best “defence” of marriage that Catholics can offer.