The biggest practical difference between the Ordinary Form and the Extraordinary is that:
1- the Extraordinary Form prayers are much longer, and generally focus a whole lot more on us being sinners and seeking forgiveness, and about the sacrifice being offerd
2- the Extraordinary Form includes a big section at the beginning called the ‘prayers at the foot of the altar’
3- the Ordinary Form is broken up into the Liturgy of the Word and the Liturgy of the Eucharist, with the homily separating the two. The Extraordinary focuses around the altar the whole time, and is divided into the Mass of Catechumens and the Mass of the Faithful, and the gospel/epistle readings are said as an aside rather than a distinct ‘focus’.
4-The Ordinary Form is more variable and has many different options the priest can choose
5-the Extraordinary Form has two distinct ‘versions’, the Low Mass and the High Mass, one having only a priest, and the High having a priest, a deacon, and subdeacon(the deacons are usually priests, they fill in the role of deacon). There is no concelebration in the TLM. The Ordinary Form does not have ‘High’ or ‘Low’ Masses.
There are many more small difference and customs pertaining to the two, but those are the biggies.
Some things that are commonly done(but not always) in the NO that are not done in the TLM:
-celebration with the priest facing towards the people
-vernacular
-lay people reading the epistles, distributing Holy Communion
-standing to recieve Communion
-no bells rung during consecration
and so on.