...the net ionic equation is....
#HO^(-) + H^+ rarrH_2O(l)#
These days, commonly, we represent the protium ion, #H^+#, in aqueous solution as...#H_3O^+#...i.e. a protonated water molecule.
The following is taken from a previous answer...
We may take a tank of #HCl(g)#, and we can bleed it in to water to give an AQUEOUS solution that we could represent as #HCl(aq)# OR #H_3O^+# and #Cl^−#.
#HCl(g) stackrel(H_2O)rarrunderbrace(H_3O^(+))_("hydronium ion") +Cl^-#
In each case this is a REPRESENTATION of what occurs in solution. If we bleed enuff gas in, we achieve saturation at a concentration of approx. #10.6*mol*L^-1# with respect to hydrochloric acid.
As far as anyone knows, the actual acidium ion in solution is
#H_5O_2^+# or #H_7O_3^+#, i.e. a cluster of 2 or 3 or 4 water molecules with an EXTRA #H^+# tacked on. We represent it in solution (without loss of generality) as #H_3O^+#, the #"hydronium ion"#, which is clearly the conjugate acid of #H_2O#. Representation of the acidium species as the protium ion, #H^+#, is also still very common.
Note that the #H^+# is quite mobile, and passes, tunnels if you like, the extra #H^+# from cluster to cluster. If you have ever played rugby, I have always liked to compare to this to when the forwards form a maul, and can pass the pill from hand to hand to the back of the maul while the maul is still formed. Of course, tunnelling, proton transfer, is more likely in a cluster of water molecules, so the analogy might not be particularly apt in that there is definite transfer of a ball in a maul, but a charge in a water cluster is conceivably tunnelled. The same applies to the transfer of an hydroxide ion. For this reason both #H^+# and #HO^-# have substantial mobility in aqueous solution, and much greater mobility in solution than ions such as #Na^+#, etc.
#H^(+) + e^(-) rarr 1/2H_2(g)#
Depending at which level you are at (and I don't know!, which is part of the problem in answering questions on this site), you might not have to know the details at this level of sophistication. The level I have addressed here is probably 1st/2nd year undergrad.........
