when the hydronium ion concentration of a solution is 1x10-4 mole per
liter, what is the pH of the solution? Is the solution acidic or
basic?

The original definition of pH is the negative of the logarithm (base
10) of the hydrogen ion (or hydronium ion) in moles per liter.  Do the
calculation.  If you know what a logarithm is, then you don't even
need a calculator to do this problem.

pH values above 7 are considered basic, while those below 7 are considered acidic.

The hydronium ion is H30+, also written as H+. A hydrogen atom is
really just a proton with an electron circling. That's one of each.
Remove the electron, you get a proton...also written as H+. With me so
far?
Okay, now the definition for an acid you probably first learned is if
it donates protons...or hydronium ions...or hydrogen ions. Same thing,
at least regarding this question. It's easier now that they're all
related.
Bases you probably first learned donate OH-. Bronsted-Lowry definition
is almost the same: rather, a base is a proton acceptor.
If you look at a base and an acid, you get OH- plus H+ = H2O. Familiar formula?
OH- accepts a proton donated by an acid to make water.
Water on its own sometimes spontaneously degrades into OH- and H+.
Very little of a sample at any one time is doing that. Very, very
little. In fact, at any time, in one mole of water, 1 * 10^-7 of it is
H+, and same for OH-. Of course in neutral water, they're the same-
you can figure out why, right?
If you have a calculator, pH is just the negative log of the molar
concentration of H+. Punch it in. 1 * 10^-7 returns an answer of 7. pH
of pure water is seven. Now the pH scale makes sense.
This should allow you to answer your own question. Answer the second
part first; just by looking at the number, you should be able to tell
if the solution's basic or acidic. Hydronium ion concentration of 1 *
10 ^ -4 is greater or lesseer than 1 * 10^-7 ? If it's greater, well,
that means more hydronium, which means more H+, or protons, whatever
you'd like to call it. That would make it acidic. If it's less that 1
* 10^-7 , then that's basic.
As for pH, punch it in to a calculator like a TI-83 to get your
answer. However, since it's just 1 * 10^-4, you really only need to
look at the exponent. Try it, you'll see why.
9I don't want to answer directly, as it seems suspiciously like a
homework question. Good luck.)

The pH is estimated from the total hydronium ion concentration. The
total H3O+ concentration have to be calculated. H3O+ comes from two
components, (1) from added acid in water and (2) self dissociation of
water. In this case, total [H3O+] = (10-4) + (10-7) = 1.001x10-4. Thus
the pH will be slightly less than 7.