Let's assume the bike is friction shifting and everything works and there are no upgrades or changes planned, it's tuned and ready to go.

1-Run the L shift lever forward, so the chain is on the small ring.
2-Run the R shift lever backwards, so you are on the easiest gear.

3-Start riding, looking for level ground, with no surprises. There are always surprises.

4-Reach down, ease the R lever forward a little, until you feel/hear the chain drop one cog. Trim so it's quiet.
4-Shift it back up, repeat 3 times. Do it a 4th time for good measure.

5-Repeat step 4 down to the next cog, then back up 1, then back up again. Repeat 3 times, do it a 4th time for good measure.

6-Repeat step 5, down to the next cog (3rd one down). Now, you are getting a feel for the distance of the lever movement, and not at a critical moment.

7-Do this up and down the rear cog, all while on the small ring up front. Practice a few times (a deserted track is great for this).

8-Now, stop the bike, move the chain to the big cog, (L lever back). Go through steps 4-7, gaining proficiency on the big ring, because if feels different.

You should do this for no less than 1 hour, 3x in one week, with a day's rest in between.

9 - Now, put the chain on the middle rear cog for a 5-sp, 3rd one down for a 6-sp. Start with the chain on the big ring.
10- Ride, and only move the L shifter, moving the chain up/down. Do this where you can ride flat and not worry about surprises.
There are always surprises.
Practice this with the chain on each cog in the rear. The differences in big ring/small ring are pronounced, but you need to be able to do this quickly.
Practice some more, so all you do is run around moving from big ring to small ring and back. You should do this for no less than 1 hour 3x in one week.

Now, pick a flat route. Start on the small ring up front, biggest rear cog. Ride. Move down through the gears, then up through the gears.
If you are confident, then move the chain to the big ring up front, and go through the gears again. Now, you are ready for surprises.

11-Approach hills, practice anticipating and shifting big ring to small ring, small cog to bigger cog, before you get there, before the bike "pauses," and stay ahead of the curve. Better to spin early than lug behind. Once you lug, you are too late; you either mash it up or you miss a shift, or worse, lose some skin on that R leg.

12-You will quickly realize that anticipation is the key to smoothness, and if you plan ahead, you will find shifting twice as easy as if you don't, maybe even more so. You will have to pay attention all the time for the first 100 miles, and kind of shake down your mind and hands before each longer ride. I highly recommend running errands, etc on the bike, get saddle/shifter time in.

13-Before you know it, you'll be like a trombone player, no-look shifting by ear, and after that, some sounds will actually surprise you, and alert you to problems. Trim is key at first, and hardly necessary later on when you get your shift throws down.

How do you ride friction to Carnegie Hall?
Practice!