I2 + KIO3 + HCl ----> KCl + ICl

Ok, this is my thinking . . . .

I^+5 + 4e^- -----> I^+1
Cl^-1 +1e^- -----> 2Cl^-1

I know that this is wrong, because the e^- are all on the same side. What am I doing wrong?

The I in I2 is zero and it changes to +1 on the right.

The I in KIO3 is +5 and it goes to +1 on the right.
The easiest way to do this is to set up two half equations.
I2 ==> 2ICl
IO3^- ==> ICl
=================
Balance those two, multiply by the appropriate numbers, add them, then cancel anything common to both sides.

Ok, here is my equation on this one.

I2 -----> I^+1 + 1e-
4e- + I^+5 ----> I^+1

4(I2 ----> I^+1 +1e-)
4e- +I^5 ----> I^+1

on this problem, the e- balance, but when I start trying to balance the equation, I am not getting the same amount of I or Cl on each side. I can add H^+ or OH- or H2O, but I don't think I can add more elements. Please help me!

I would do it this way.

I2 ==> 2ICl
IO3^- ==> ICl
===================
You CAN add ions if they are spectator ions (they don't change oxidation state) and you want a molecular equation instead of an ionic equation.
For I2 ==> 2ICl
I2 is zero on the left: +1 on the right(for each) or +2 for both. (That's the first mistake you made). Now we add electrons.

I2 ==> 2ICl + 2e

Now I would add the Cl^- like so.
I2 + 2Cl^- ==> 2ICl + 2e
Adding 2Cl^- is the only way to get them into the equation.

Charge on left is -2 (from 2Cl^-) and on the right is -2 (from 2e) and this half is balanced.

The other one is the following and you need to do it. Here is what you should get.
6H^+ + 4e + Cl^- + IO3^- ==> ICl + 3H2O

Following those steps I wrote in the previous problem will get these things done almost every time. I have found, through the years, one or two that I've had trouble with when I use this method.

It seems like you are trying to balance the half-reactions for the oxidation and reduction reactions in the given chemical equation. However, there is a mistake in your approach.

When balancing half-reactions, it is important to ensure that the number of electrons (e-) on the reactant side is equal to the number of electrons on the product side. In your current attempt, you have written different numbers of electrons on each side.

To properly balance the half-reactions, you need to identify the oxidation state changes for the elements involved. In this case, iodine (I) is going from an oxidation state of +5 to +1, while chlorine (Cl) remains at an oxidation state of -1.

The balanced half-reaction for the reduction of iodine can be written as follows:

I^+5 + 5e^- → I^+1

Since there is no change in the oxidation state of chlorine, the half-reaction for the oxidation of chloride is as follows:

Cl^-1 → 2Cl^-1 + 2e^-

Now, the number of electrons on both sides of each half-reaction is equal. By multiplying the equations by suitable factors, you can balance them so that the total number of electrons gained and lost is the same.

Finally, it's worth mentioning that the balanced half-reactions need to be combined appropriately to balance the overall chemical equation.