The word modernism is a bit of a misnomer. After all, how can something that was described by Pope Pius X as the synthesis of all heresies be anything but ancient? Moreover, the word seems to imply an excessive attachment to innovations and progress. This is not the case because the essential definition lies with one's attitude towards dogma. Modernism is characterized by a willingness to pervert dogma in an effort to make it conform to one's own notion of progress or the spirit of the age. It is the twisting of dogma that is the identifying characteristic of modernism, not the presence of innovations. Appearances can be deceiving as Cardinal Ferrari pointed out in 1908:
We are deeply pained to find that certain persons, in public controversy against modernism, in brochures, newspapers and other periodicals, go to the length of detecting the evil everywhere, or at any rate of imputing it to those who are very far from being infected with it. CE
This association of modernism with innovation has led many to indiscriminately toss the epithet about. However sometimes there are changes which are badly timed, poorly carried out or taken to extremes. There are treasures in the Church's store which have been sorely neglected. Badly done liturgy has been with us for a very long time. However bad these things are, none of them in themselves cut to the core of the issue. The smoking gun with modernism is the perversion of doctrine and unless you have identified that core problem you have nothing in hand at all.
Here, however, it is needful to speak a word of warning against unreasonable attacks. Not every novelty is to be condemned, nor is every project of reform to be dubbed modernist because it is untimely or exaggerated. CE
One more thing needs to be said about modernism and that is its use of language. You will notice the words with which I have described the modernist attitude towards dogma. I have described it as a perversion or as a twisting. In the past heresies were characterized by a picking and choosing of one doctrine over another. The word comes from the Greek and means to choose or a choosing. Each party in the controversy believed that they were dealing with divine revelation and their differences consisted of a disagreement over the content or interpretation of that revelation. Modernism is different in that it attempts to adhere to the terms the Church uses to define dogma while subtly changing their meanings to suit whatever their agenda is. Thus the Oath Against the Errors of Modernism rejects these misinterpretations and changes in meaning.
Fourthly, I sincerely hold that the doctrine of faith was handed down to us from the apostles through the orthodox Fathers in exactly the same meaning and always in the same purport. Therefore, I entirely reject the heretical' misrepresentation that dogmas evolve and change from one meaning to another different from the one which the Church held previously.
The bottom line here is that if one is rejecting one or another doctrine of the Church, one is not a modernist but a protestant, but more on that in another post. Modernists do not wish to leave the Church and will go through all sorts of contortions to seem to conform.
On the other hand, it is regrettable that certain avowed leaders of modernism, carried away perhaps by the desire to remain within the Church at all costs — another characteristic of modernism — have taken refuge in equivocation, reticence, or quibbles. Such a line of action merits no sympathy; while it explains, if it does not altogether justify, the distrust of sincere Catholics. CE
How then should the ordinary Catholic recognize modernism? The guitar group at the folk mass may be playing music that is modern and out of keeping with the Church's tradition, but are they modernist? Well, you are not likely to find out without talking to them and looking for the perversion of dogma. However, it may well be a case of bad taste. How about the parishioner who wishes wistfully that she or someone like her might be ordained a priest someday? Definitely a modernist inclination there because what she is really saying is that the papal pronouncements on women's ordination are subject to change over time. "Just keep up the pressure, they're bound to change eventually." Even conservatives are not immune from this tactic.
Unfortunately the word modernism has so degraded over time that few Catholics are likely to know what you are talking about except to note that you have called them something bad. This is why recent pronouncements by Benedict XVI have used words like relativism and secularism to describe this phenomena. As he said in his homily before the conclave that elected him:
To have a clear faith, according to the creed of the Church, is often
labeled as fundamentalism. While relativism, that is, allowing oneself
to be carried about with every wind of "doctrine," seems to be the only
attitude that is fashionable. A dictatorship of relativism is being
constituted that recognizes nothing as absolute and which only leaves
the "I" and its whims as the ultimate measure.
CE - Catholic Encyclopedia, 1917 ed., www.newadvent.org