The Tridentine Mass has a whole set of venerations and adorations, so I will list each one in sequence used for a Solemn High Mass:
Clerical Processional [Stand]: The priest and altar boys start to process when the bell rings. Sometimes they will go outside and to the front door, then walking up the center aisle. They may also enter via the side aisle and up down through the nave. When the crucifix passes you, genuflect and make the Sign of the Cross.
Asperges [Kneel, stand when sprinkled]: The priest, in a cope, will kneel at the foot of the altar, and intone the antiphon "As-pe-r-ge-s-me". The schola will sing the rest of the hymn. Meanwhile, the priest will sprinkle the altar and the congregration, acompanied by the deacon and subdeacon. When the antiphon is finished, the priest will chant the concluding prescription prayers.
Vesting for Mass [sit]: At this time the priest will remove his cope and put on the chasuble and maniple; the deacon and subdeacon will add maniples on their left arms as well. This is done at the sedilla (priest's bench or chair). The chasuble is left on the sedilla for its anticipated use for Mass following the Asperges.
Prayers at the Foot of the Altar
Incensing of the Altar, Introit, and Kyrie [kneel]: These include the Sign of the Cross, Psalm 42, and the Confiteor. Make the Sign of the Cross when the priest does so. The priest and servers will recite the prayers softly (as as done through most of the Mass) while the schola sings the Introit and Kyrie. Recite the Confiteor to yourself when the servers do so, and make sure you mea culpa. The priest will read the introits and and the Kyrie at the Epistle side of the altar.
Gloria [stand, sit when priest sits]: The priest will proceed the the center of the altar and will intone "Glor-i-a-in-ex-cel-sis-de-o". The priest and servers will recite as the schola sings. When the priest is finished, he will sit down, so then you may sit down. He will be wearing his biretta at the sedilla, so when Jesu Christe is sung, he will take his hat off. At this time, it is very appropriate to strike your breast.
Collect(s) [stand]: The priest will then proceed to the center of the altar and intone Dominus vobiscum..., etc. Collects are said at the Epistle side.
Epistle [sit]: At this time the subdeacon will stand on the Epistle side of the sanctuary and chant the Epistle. At the end, you may say "Deo gratias", but is not to be said aloud. The subdeacon will go to the priest and have the book blessed.
Gradual and Alleluia (or Tract) [stand]: The priest will proceed to the Epistle side of the altar to read these, while the schola chants them.
Gospel [stand]: The Gospel is chanted on the north side of the sanctuary by the deacon, with the subdeacon holding the book. the gospel will be incensed. After the small Sign of the Cross is made, it is very appropriate to place your right hand over your heart. These are Jesus' words, and thou shalt live by them. Even though it is not in the rubrics to do so, the faithful should do it as a devotion before Holy Communion, even though it is a ways off in the Mass that the host and chalice are mentioned.
Sermon: After the Gospel "blots away our sins", the priest will genuflect at the altar, place his maniple on the missal, and proceed to the pulpit. Before giving the actual sermon (or homily), the priest will generally reread the Epistle and Gospel in the vernacular (in my case, in English). The posture rules are the same (as above) as if they were chanted in Latin. Then the priest might offer prayer intentions and parish announcements, if appropriate.
Credo [stand, sit when priest sits]: Rules are the same as the Gloria, but genuflect at the Virgin Mary line.
Offertory and Lavabo [sit]
Orate Frates, Secret(s), and Preface [stand]
Sanctus and Canon [kneel]: Strike breast when bells ring and when sacred species are consecrated.
Pater Noster to Kiss of Peace [stand]: Do not hold hands or make any sign of peace. The priest will sing the Our Father until the "temptationum", and the schola will sing "Sed-lib-ra-nos-a-mal-o." The Kiss of Peace is only reserved for clergy in a state of grace. In the Novus Ordo, a Protestant addition to the Our Father is added, and should not appear in the Mass because it is from the King James Bible, which is not approved by the Roman Catholic Church. Therefore, the actions at the New Mass, including the priest shaking hands with the altar boys, is scandalous since the priest cannot touch anything else with his thumbs and index fingers except for the sacred species. This ensures the protection of sacrilige of the Body, Blood, Soul, and Divinity of Our Lord Jesus Christ.
Agnus Dei [kneel]
Communion of the Priest [kneel]: Please note that in the Extraordinary Form, the priest, nor the deacon or subdeacon, does not open the tabernacle until the celebrant consumes the host and precious blood.
Communion of the Faithful [kneel, stand to walk to altar rail, etc.]: In the 1962 typical edition of the Missale Romanum, there is no instruction to have the Confiteor recited by the servers before the priest turns around and shows "Ecce Agnus Dei". However, during the High Masses that I go to in the Archdiocese of Boston, the Confiteor is chanted by the deacon, followed by the priest giving a general absolution. Eariler editions of the missal have a Confiteor before Holy Communion, so this may be up to each bishop whether he wishes that the Confiteor be said before Communion or not during the Extraordinary Form. There is no such confession in the Novus Ordo.
When you receive Holy Communion, besides kneeling, you should have your right hand crossing your heart, with the left hand covering the right hand. [See pictures of the Annunciation of the BVM if you want a visualization.] When the priest or deacon is serving the person to your right, make sure you close your eyes so that your tongue will stick out so the sacred minister will say "Corpus Domini nostri Jesu Christi custodiat aman tuam in vitam aeternam. Amen". [May the Body of Our Lord Jesus Christ bring us into eternal life. Amen.]
When Holy Communion is in your mouth and on its way toward your heart, make the Sign of the Cross, open your eyes, cross your heart again, and walk back to your pew. Kneel in your pew until the bell rings, which means that the hosts are reposesed in the tabernacle. You may sit at this time if you wish.
Postcommunion prayer(s) [stand]: See the rules for the Collects.
P. Dominus vobiscum.
S. Et cum spritu tuo.
S. Deo gratias.
Blessing [kneel]: The priest will say a prayer to the Most Holy Trinity, and then will turn around to bless the people "Patris, et Filli, et Spritus Sancti. Amen."
Last Gospel (John 1:1-14) [stand]: It is not necessary to cover your heart for this Gospel, but you must make the small Sign of the Cross and genuflect at "Et carnate homo est." The Last Gospel is said to the priest inaudiby.
[During Low Mass the Leonine Prayers will be recited at of the foot of the altar here.]
Recessional: Stand when the clergy leave the church for the sacristy. The sacred ministers will wear their birettas during the procession. It is considered in poor taste to leave before the music ends, never mind when the clergy are gone. So do not leave until (1) the music is done, and (2) the clergy are not in the main church/worship space.
After Mass: You may kneel after Mass to recite the Rosary of the Prayers of Thanksgiving after Mass; please see your missal for more details.
Please note that I have never seen the priest greet the people at the back door after a Tridentine Mass. When the recessional ends in the sacristy (or vestry), the priest will give an "exit blessing" to the servers. Most likely, the priest, deacon, subdeacon, and the altar boys will unvest from mass to choir dress. Since the deacon and subdeacon are generally ordained priests, they will place a reversable sacramental stole on for blessings, Confessions, Extreme Unction, or a baptism scheduled after Mass. Here is the time to see the priest in the sacristy to seek a blessing, or to make other sacramental arragements.