How would I return a random Mathematica command?

There are a lot of commands! One way to get a list is to use Names["*"], which will return all the symbols Mathematica knows. Since commands start with capital letters, you can gain more control over the list by asking for only a subset. For example,

all = {"A*", "B*", "C*"};
Names[#] & /@ all

provides a list of all commands that start with A, B, or C. You could customize the all to suit your preferences.

Get the full list of Mathematica functions here:

myFunctionList = Import["http://reference.wolfram.com/language/guide/\
AlphabeticalListing.html"];

Strip the list of header and footer material, and select a random element:

RandomChoice[StringSplit[StringTake[myFunctionList, {3245, -1225}]]]

Or, based on the approach of bill s:

RandomChoice@Flatten[Names[#] & /@ (StringJoin[#, "*"] & /@ CharacterRange["A", "Z"])]

Here's a piece of code that lets you see random Wolfram Language code snippets, rather than just command names.

RandomExample[] := Module[{dir, file, inputs, output, cap, i = 0, j = 1, in},
    dir = DirectoryName[FindFile["ExamplePages/CreateMolecularGraphs.nb"]];
    file = RandomChoice[FileNames["*", dir]];
    output = Import[file, {"Cells", "Output"}][[1]];

    cap = CellLabel /. Options[output];
    If[!StringQ[cap], Return[$Failed]];
    cap = ToExpression[StringReplace[cap, "Out[" ~~ x__ ~~ "]" ~~ __ :> x]];

    inputs = Import[file, {"Cells", "Input"}];

    CellPrint[TextCell[
        StringReplace[file, __ ~~ "ExamplePages" :> "ExamplePages"],
        "Subsubsection"
    ]];

    CellPrint[Reap[
        While[i < cap && j <= Length[inputs],
            in = CellLabel /. Options[inputs[[j]]];
            If[StringQ[in],
                i = ToExpression[StringReplace[in, "In[" ~~ x__ ~~ "]" ~~ __ :> x]]
            ];
            Sow[inputs[[j++]]]
        ]
    ][[-1, 1]]];

    CellPrint[output];
]