Music and lyrics are passed aurally/orally, and were rarely written down until recently (depending upon your definition of "recently", there are many examples of written music previous to the 1800's). Though solo performance is preferred in the folk tradition, bands or at least small ensembles have probably always been a part of Irish music since at least the mid-1800's, although this is a point of much contention among ethnomusicologists.
For instance, guitars and bouzoukis only entered the traditional Irish music world in the 1960's. The bodhran, once known in Ireland as a tambourine, is generally first mentioned in the 1800's. Ceili bands of the 1940's often included a drum set and stand-up bass as well as saxophones. As of current writing, the first three are now generally accepted in traditional Irish music circles (although not in the most purist of venues), while the latter three are generally not.
More recently, traditional Irish music has been "expanded" to include new styles and variations performed by bands, although arguments run rife as to whether you may then call this music "traditional". Unaccompanied vocals in the sean nós; (which means, simply, "old style") tradition are considered the traditional norm, usually either solo or as a duo. Harmony is simple, and instruments are played in unison. Counterpoint is mostly unknown to traditional music. Structural units are symmetrical and include decorations of the rhythm, text, melody and phrasing, though not usually of dynamics, due to instrumentation issues while Irish music was developing.
Irish traditional music was largely meant (to the best of our current knowledge) for dancing at celebrations for weddings, saint's days or other observances. Tunes (songs have words, tunes do not) are most usually divided into two eight-bar strains which are each played twice to make a 32-bar whole; Irish dance music is isometric. (16 measures are known as a "step", with one 8 bar strain for a "right foot" and the second for the "left foot" of the step.) Tunes that are not so evenly divided are called "crooked".) This makes for an eminently danceable music, and Irish dance has been widely exported abroad.
Traditional dances and tunes include reels, hornpipes, jigs and slip jigs, as well as imported polkas and mazurkas.
Set dancing, generally danced by groups of varying sizes (a "set" is a group of a certain number of dancers), is one of the most popular of the Irish traditional dances, revived along with other Irish cultural forms, during the Celtic Revival period of the 1800's, and again re-popularized after the success of the Broadway-style musical Riverdance in 1994. It is not uncommon for young people in Ireland's cities (and other large cities around the world) these days to go set-dancing as others of their contemporaries go "clubbing".
Stepdancing, in the Munster or southern style form, is the most widespread of the Irish dance forms, although there are many others (including the Connemara style and other forms of Southern style dancing not under the auspices of An Coimisiun). Modern stepdancing is connected to the Irish cultural revivals of the 1800's in one long line. Modern stepdancers are athletes as well as dancers; champions train in a manner similar to ice skaters and gymnasts. It is largely a solo dance form, although group dances or figures exist in a set curriculum of ceili, or party, dances.
The litmus test of the solo stepdancer is the non-traditional set dance (not related to set dancing, where groups of dancers form figures) which is generally choreographed by a dancer's teacher for that dancer or for the teacher's dancing school.
No modern description of the arts of Ireland would be complete without some mention of the Broadway musical Riverdance. A musical and dancing interval act starring Michael Flatley and Jean Butler was performed during the 1994 Eurovision Song Contest. Popular reaction to the act was so immense that an entire musical was built around the act. Riverdance's appeal was such that the arts of Ireland were once again globally popular in a very short time. Dancing school enrollments skyrocketed, Irish sessions found their numbers swelling with new musicians wishing to take part, and interest in Irish arts are at an all time high.
It is important to know that most "traditions" of modern Irish traditional music and dance are, to some extent, guesswork and extrapolation. Through politics and military upheavals, the cultural arts of Ireland were systematically eradicated to a large extent (to weaken national identity) and then the job was finished during the Great Famine. Travellers (the gypsies of Ireland, most of whom began their dynasties when forcibly ejected from their lands; they call themselves the Pavee), people (covertly, during periods of active occupation) trying to save knowledge from eradication, and refugees saved what we know of languages and artforms.
Regional style, once a major distinction of Irish traditional music, is gradually being eroded by the ease of travel and access to recordings. It was once not unheard of for a villager to never leave the immediate area of their village; in those days, you could often tell the region an Irish player came from by simply his playing or the setting of a tune used.
Singing often is seen as something very different from the music. This can be seen in many sessions in pubs in Ireland. While the musicians are playing, the rest of the gathering may treat them as largely background music. When a singer is invited to sing, however, there is generally not a sound to be heard other than murmurs encouraging the singer. Oftentimes, listeners may sing along with choruses. There is a type of traditional song called loobeen, in which each singer improvises a verse, followed by a chorus sung by the entire group. It is generally felt among traditionalists that the music is largely for amusement, while songs distill within them the true spirit of Ireland.
Flutes and whistles -- Flutes have long been an integral part of Irish traditional music, and its cousin the tin whistle or low whistle are also popular. Modern flautists include Matt Molloy, Kevin Crawford, Michael McGoldrick, Desi Wilson and Emer Mayock, while whistlers include Paddy Moloney, Sean Ryan, Mary Bergin and Packie Byrne.
Accordion and concertina -- The accordion plays a major part in modern music. Popular players include John Williams, Sharon Shannon and Dave Hennessy. Concertina players include Niall Vallely and Noel Hill.
Bouzouki -- A fairly recent import from Greece, the bouzouki was introduced in the late 1960s by Johnny Moynihan and then popularized by Donal Lunny, Andy Irvine, and Alec Finn.
Fiddle -- One of the most important instruments in the traditional repertoire, the fiddle is played differently in widely-varying regional styles. Modern performers include Martin Hayes, Paul Shaughnessy, Matt Cranitch, Frankie Gavin, the Glackin brothers, Mairéad Ní Mhaonaigh, and Tommy Peoples. Sligo fiddlers like Michael Coleman did much to popularise Irish music in the States in the 1920's.
Uilleann pipes -- A king of bagpipes, uilleann pipes are complex and said to take years to learn to play. Its modern form had arrived by the 1890s, and was played by gentlemen pipers like Seamus Ennis in refined and ornate pieces, as well as showy, ornamented forms played by travelling pipers. Liam O'Flynn is one of the most popular of modern traditional performers along with Paddy Keenan, John McSherry and Mick O'Brien and many more.
Bodhrán; -- A frame drum, the bodhrán is considered a relatively modern addition to traditional dance music. It was introduced in the 1960s by Sean Ó Riada;, and quickly became popular. Great players include Johnny 'Ringo' McDonagh and Colm Murphy.
Harp -- Played as long ago as the 8th century, the harp is a symbol of Ireland and its players are widely-respected. Many tunes were written by Turlough Ó Carolan;, a blind 18th century harpist who is considered by many to be the unofficial national composer of Ireland. Modern traditional players include Laoise Kelly, Máire Ní Chathasaigh; and Bonnie Shaljean. Irish harp music is built around particular chords of the scale.
A movement of revival took place (based in London and Dublin) in the early 1900's. A commission was formed, and the arts encouraged. The public was invited to actively take part, and a great passion was discovered for the arts of Ireland.
The uillean pipes play a prominent part in a form of instrumental music called Fonn Mall, descendents of ancient songs, as well as in the unaccompanied vocal music called sean nós;. Willie Clancy, Leo Rowesome, and Garret Barry are among the many pipers famous in their day. Tony McMahon, Davy Spillane and Robbie Hannon play these traditional airs today, among many others. Many Pavee families, such as the Fureys and Dorans and Keenans, are famous for the pipers among them.
The history and future of cultural arts of Ireland, like the island itself, is filled with contradictions and passionate opposing viewpoints. This is how it's always been, and hopefully always will be.