"Show me!"

So Tetsuma does, starting with a nice, calm lake that has a reasonable temperature, having already double checked with the locals that it's safe to swim.

Okay... what should she do?

Tetsuma explains as best he can, but there's still going to be a lot of trial and error building off the 'channel chakra to your feet' lesson from tree climbing. But instead of focusing on a steady flow of chakra, she'll need to adjust to the water as it changes, and be trying to push off ever-so-slightly while also sticking.

...He'd also recommend not wearing anything that can't get wet. She's going to be falling in. A lot.

She strips to her underwear, then.

Ahhhhhhhhhhhhhh

Okay Tetsuma's going to be teaching while blushing furiously.

She will probably fall into the water a few times.

Yeah 'a few' is a low estimate here. Still, for someone with decent chakra control and enough stubbornness, it's not ludicrously hard.

She has at least one of those things!

Her chakra control must also be pretty good to be so talented at genjutsu. Though it's still probably very fortunate that Tetsuma picked a shallow lake.

Eh, she can swim, but yeah that could get old fast.

Tetsuma meditates while Dayo practices, and works some on his wood manipulation. Practice shaping wood finely, mostly.

This is extremely tiring.

Yeah, it's pretty exhausting until you get good at it. Though Dayo will probably notice her control improving slightly as her chakra reserves run down. Tetsuma packed a large lunch, though, and they can take plenty of breaks.

Breaks! Kissing!

Definitely kissing during breaks!

She'll probably be able to at least stay upright for a bit by the time they have to go.

Almost certainly. (Tetsuma shows off a bit by running around, then picking up Dayo while standing on the lake, if she seems amenable.)

"Show-off," she accuses, kissing him on the cheek.

Eee!

"Maybe a little." He snorts. "Back home, showing off was unladylike." He gives a little twirl, kissing Dayo. "I find I like being unladylike. You, ma'am, have been a bad influence on me." More kisses!

So many kisses! "I care so little about what is or isn't ladylike, you wouldn't even know."

"I like that about you! Learning proper behavior is worse than math."

She gasps in mock horror. "You dare insult math?"

"Math is the bane of my existence."

"I'm sorry Tetsuma but I think we must break up. I could not possibly date someone who dislikes math." She puts a hand in front of her mouth and looks around as if checking for anyone who might be overhearing such blasphemous words.