First things first. The Baronius Press edition (that I use) is notorious for errors in the early printing. Check the first couple of pages for a date. If it’s around 2010-2011 it should be fine. But to double check look at Lauds in Office 3. The Little Chapter and Hymn should be the same as Office 1. My printing has the Ave Maris Stella which is wrong. The first verse for Compline’s hymn is wrong in the Latin. It should be Memento Rerum, not O Gloriosa. It’s only the first verse though and the English is fine. Office 2 and 3 None is a wreck. The Antiphon’s are right but the Little Chapter and Versicle and Response is mixed up. You need to read Office 2 None for the Little Chapter and Versicle and Response for Office 3. The Antiphons for Office 2 and 3 Lauds are mixed up as well. But that’s only my edition. Yours might be corrected.
Now all that out there. Matins, Lauds, Prime, Terce, Sext, None, Vespers and Compline. These are the Hours. Matins at Midnight, Lauds at 3am-Dawn. Prime at 6am. Terce at 9am. Sext at 12pm. None at 3pm. Vespers at 6pm-Evening. Compline at 9pm-before bed. I suggest just sticking with Lauds (when you wake up), Vespers (after supper) and Compline (your bed-time prayer) as a beginner.
I’m sure you’re aware of the general make up of the Hours. At least three Psalms, a hymn, a Little Chapter, etc. The three major Hours I suggested above also have Canticles (such as Our Lady’s Mangificat). These are marked with a red cross at the beginning where you make the sign of the cross (though the Nunc Dimitis at Compline doesn’t have this printed, do it anyway!).
Basically, you just go right through it. Take your time. You don’t have to announce Psalm numbers or the Little Chapter readings. You just reading through it (and recite it!). The Office is actually intended to be sung, and if you can chant, good! I can’t so I just speak the Hours

! There are ceremonies for reciting the Office in choir. Kneeling at certain places, etc. Private recitation isn’t as stict. I only observe bowing during the Gloria Patri and the signs of the cross. Otherwise kneel, stand and sit as you feel comfortable.
There are also Collects at the end. Collects have endings (through the same Jesus Christ Our Lord, etc.) at the end of the collect. They’re very rarely given in full. And sometimes the words are jumbled at the end, given a different arrangement, etc.
We’re in Office 3 right now, and the collects are the same for every Office. The ending is “qui tecum vivit et regnat in unitate spiritus sancti Deus, per omnia saecula saeculorum. Amen.” Occasionally the “filium tuum” is dropped after the Jesum Christum in some of the collects, it should’t be though.
So, Office 3. Lauds and Vespers are given in full. Compline you start with Compline in Office 1. When you come to the Little Chapter, you switch to Office 3 (which also contains the antiphon for the Nunc Dimittis in Christmastide). Then do the Office 3 collect and conclude by turning back to Office 1 to finish Compline.
Two notes. First at the Aperi, before the Office. You make the cross on your lips and heart (like at the gospel) though without the forehead. Same with the heart at the Coverte nos at Compline. Secondly, after a Versicle and Response with the Little Chapter, before the Collect, there’s another Versicle and Response. “Domine, exaudi orationem meam. Et clamor meus ad te veniat.”. This isn’t printed in the Office 2 and 3 propers. But always say them before the Collect.