Build a dirt house using only dirt, give yourself a time limit, like 3 hours so that it would be harder to build. If you fail you must give your friend your wooden hoe, if you still don't have a wooden hoe (they're hard to come by) you must make one for your friend.
I have played for years and I still struggle to build a dirt house under 3 hours.
First you need to decide what kind of underground city you want…
Often "underground city" is taken to mean city-in-a-cavern; building a more or less conventional city on the floor of a verrry large cave.
It can also mean a cave with the 'buildings' cut into the walls (so that they only have fronts).
Whether or not there is a central column / pillar and whether the 'buildings' are in the center or around the periphery (or both) is another design question.
If there is not a column / pillar, there may be some other central feature such as a pit or lake (water or lava).
Finally, an "underground city" can be built with the 'buildings' cut into the walls of a series of interconnected tunnels without any large open space. [Note this option will preclude much in the way of viewing the city as a whole.]
As to what sort of buildings to create… peoples needs don't change: they need;
safety (i.e. doors, moats, etc)
food (and places to grow, store, and prepare it)
water (well not technically in MC )
places to sleep
municiple buildings (i.e. town hall, library, jail, religious / cultural areas, etc).
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.