As orthocresol suggested, to illustrate "classic" acidity as it's understood on a school level you unquestionably want to start with Arrhenius definition, which attributes acidic properties to any substance which increase concentration of hydronium $\ce{H3O+}$ ions in water.
That's said, the very first reaction you probably want to write is dissociation of $\ce{H2S}$ in water and demonstrating that it is a weak acid by showing the corresponding acid dissociation constants $K_\mathrm{a}$ (the larger the $\mathrm{p}K_\mathrm{a},$ the weaker the acid; data from [1, p. 5-87]):
$$
\begin{align}
\ce{H2S + H2O &<=> HS- + H3O+} &\quad \mathrm{p}K_\mathrm{a1} &= 7.05\\
\ce{HS- + H2O &<=> S^2- + H3O+} &\quad \mathrm{p}K_\mathrm{a2} &= 19
\end{align}
$$
Some reactions illustrating acidic properties of $\ce{H2S}$:
Reaction with sodium hydroxide
Note that the reaction
$$\ce{H2S(aq) + 2 NaOH(aq) -> Na2S(aq) + 2 H2O(l)}$$
is for complete neutralization (concentrated $\ce{NaOH}$ solution).
If the reactants are taken in 1:1 ratio (diluted $\ce{NaOH}$ solution), sodium hydrosulfide is formed:
$$\ce{H2S(aq) + NaOH(aq) -> NaHS(aq) + H2O(l)}$$
Reaction with sodium carbonate
Sodium hydrosulfide is also formed when saturated $\ce{H2S}$ solution reacts with $\ce{Na2CO3}$:
$$\ce{H2S(aq) + Na2CO3(aq) -> NaHS(aq) + NaHCO3(aq)}$$
Reaction with ammonia
Reaction with aqueous ammonia solution yields exclusively in ammonium hydrogen sulfide $\ce{NH4HS},$ even when concentrated ammonia solution is used:
$$\ce{H2S(aq) + NH4OH(aq) -> NH4HS(aq) + H2O(l)}$$
Ammonium sulfide $\ce{(NH4)2S}$ doesn't form as ammonium $\ce{NH4+}$ $(\mathrm{p}K_\mathrm{a} = 9.25)$ is a much stronger acid than hydrosulfide $\ce{HS-}$ by a factor of about $10^{19 - 9.25}\approx\pu{6E9}.$
So far the reactions between well-soluble compounds that were carried in aqueous solutions where Arrhenius definition works fine.
However, it cannot be used to explain acidity in non-aqueous media, where a Brønsted–Lowry definition of an acid comes in handy: the acid is a proton donor.
This can be illustrated by the reaction with liquid ammonia:
$$\ce{H2S(g) + 2 NH3(l) ->[\pu{-40 °C}] (NH4)2S(s)}$$
References
- Haynes, W. M.; Lide, D. R.; Bruno, T. J., Eds, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data; 97th Edn.; Taylor & Francis Group (CRC Press): Boca Raton, FL, 2016-2017. ISBN 978-1-4987-5429-3.