Wow, didn't know that..
On my vintage B&S the oil drain plug is under the deck, near the blade shaft.
Yes, the old ones had the drain plug and if you look on the one you have the aluminum boss is still there they just decided to not drought the hole tap it and insert the pipe plug somewhere back around 97 or so maybe as late as 2001 but somewhere in that vintage they stop putting drain plugs in all the small push mower vertical engines.
As others have mentioned sucking it out can be done too but I find that not to be the best way as you typically leave more oil in it.
It's my preference to run the engine for 4 or 5 minutes so you will get all the particles and dirt and suspension because otherwise the sludge part will stay down in the bottom and you won't get that out as much. After it runs for three or four minutes, just flip it over into a pan.
Some machines like edgers and blowers could be a little harder to maneuver so you might need another person but the standard 21 or 22 in push mower is very easy just to flip over into a pan.
You'll get really good at doing it especially on the push mowers and you'll find the exact sweet spot so it rests right on the edge of the plastic drain pan but not touching the muffler which could still be hot from running.
Otherwise, you'll start to melt your pan a little bit. I use those cheap plastic drain pans because I can get them to the dollar store for $1.25. used to be a dollar but you know still cheaper than the parts stores or walmart.
In actual practice though, it would be better for me to pick up a metal version of the same thing because then I could use indefinitely and they wouldn't eventually crack and have to be replaced.
I certainly prefer the style like you have that has the dipstick because some of the smaller cheaper engines and the newer cheaper ones don't even have a dipstick that comes to the top like that so it makes a mess and runs down the side of the deck. This style I'm so accustomed to that I can actually flip the mower over towards me and hold even a small mouth milk jug and fully drain the oil without spilling a drop and I don't even need a pan. It's even easier if you have one of the empty 5 quart oil jugs with the larger mouth.
I typically still use the pan though and then since I like to get all of it out I will stand above the mower on the bottom side of it and pick it up and tilt it a little bit this way in that to get the extra ounce or two of all out of it.
And then remember, the most important thing it only holds 20 oz of oil. Do not overfill.
He should also be a straight SAE 30 or hd30 oil and not a multigrade and not a synthetic because that's just not necessary and you're going to have increased oil consumption or leaks with it and you're only going to find a 5:30 or 10:30 synthetic and not a straight weight even though amsoil will claim that one of their oils is the same for a 30 and a 10w30.
Just never use indie or non detergent oil. They need to quit selling that stuff in the normal stores because nobody really understands what it's for.
That stuff hasn't been used in an internal combustion engine since around 1953 and it shouldn't be.
The dumb merchandisers at the department stores especially Walmart actually put it on the shelf almost next to the two cycle oil implying that it belongs in the outdoor power equipment arena which it does not!
That stuff should only be used for oiling a bronze bearing sleeve or a fan motor and even at that 30 weight is too thick. Most of the appropriate oils for those situations are much higher quality and cleaner and almost clear compared to an ND 30 and most are 10 to 20 weight.