Could you please explain to me how to balance a chemical equation? I've been trying to figure it out, but I can't seem to understand it at all.

There are two types of equations to balance.

1)non-redox which are balanced by trial and error.
2) redox equations which have rules that can be followed (although sometimes they can be balanced by trial and error also).
I assume you want #1. Here is a simple one.
CH4 + O2 ==> CO2 + H2O
1. I look at the equation and just start with the first element. C is 1 on the left and 1 on the right. Temporarily, at least, this one is ok for now unless something else changes it.

2. Then I look at H. There are 4 atoms on the left and I can make it 4 on the right by adding a coefficient of 2 for H2O so now the equation looks like this.
CH4 + O2 ==> CO2 + 2H2O

3. When balancing oxygen, I notice it stands by itself; therefore, I NEVER try to add O2 and try to balance it on the right. I ALWAYS count up what I need on the right, then make the one on the left the number I need. On the right I have 4 O atoms (2 from CO2 and 2 from 2H2O = 4). So I need 4 on the left and I can get that by placing a coefficient of 2 for O2 so the balanced equation reads as
CH4 + 2O2 ==> CO2 + 2H2O.

4. I ALWAYS check it to make sure it is right. I see 1 C on left and right.
I see 4 H atoms on left and right.
I see 4 O atoms on left and right. Equation is balanced.

5. How do you get more proficient at this? Practice, practice, practice.

Certainly! Balancing a chemical equation involves making sure that the number of atoms of each element on both sides of the equation is the same. Here's a step-by-step guide to help you balance a chemical equation:

Step 1: Write Down the Unbalanced Equation
Start by writing down the unbalanced equation. For example, let's balance the equation for the combustion of methane: CH4 + O2 -> CO2 + H2O.

Step 2: Count the Number of Atoms on Each Side
Count the number of atoms of each element on both sides of the equation. In our example equation, there is 1 carbon (C) atom on the left side and 1 carbon atom on the right side. There are 4 hydrogen (H) atoms on the left and 2 hydrogen atoms on the right. There are also 2 oxygen (O) atoms on the left and 3 oxygen atoms on the right.

Step 3: Balance the Most Complex Atom First
Start by balancing the atoms that appear in the fewest compounds or are the most complex. In our example, we'll balance carbon (C) first.

To balance the carbon, we need to add a coefficient in front of one of the compounds. In this case, we'll add a "2" in front of CO2 on the right side of the equation. The equation now becomes: CH4 + O2 -> 2CO2 + H2O.

Step 4: Balance the Next Element
Next, move on to a different element and balance it. In our example, let's balance hydrogen (H).

There are 4 hydrogen atoms on the left side, but only 2 hydrogen atoms on the right side. To balance hydrogen, we'll add a "2" in front of the H2O on the right side. The equation now becomes: CH4 + O2 -> 2CO2 + 2H2O.

Step 5: Balance the Last Element
Finally, balance the last element, which in our example is oxygen (O).

There are 2 oxygen atoms on the left side, but now we have 4 oxygen atoms from the CO2 and 4 oxygen atoms from the H2O on the right side. To balance oxygen, we need to adjust the coefficient in front of O2 on the left side. In this case, we'll add a "2" in front of O2. The final balanced equation becomes: CH4 + 2O2 -> 2CO2 + 2H2O.

Step 6: Check and Simplify (if necessary)
Check if all the atoms are balanced and simplify the equation if possible. In our example, both sides have 1 carbon atom, 4 hydrogen atoms, and 4 oxygen atoms, so it is balanced.

If needed, you can simplify the equation further by dividing all coefficients by their greatest common divisor. In this case, it remains as it is.

That's it! Following these steps should help you balance any chemical equation.