Ok the only way you will learn to balance equations is to practice by doing problems. There is no silver bullet, there is no algorithm, you just have to practice over and over. If you can't balance equations, you won't get far in chemistry (I think you are aware of this). Look in your general chemistry textbook and work problems. Look on google for practice problems. Do whatever you have to do to learn this.
And by the way, expect a little trial and error with these problems.
Ok let's look at the combustion of butane:
C4H10 + O2 => H2O + CO2
ON THE LEFT SIDE of the equation we have:
4 atoms of CARBON
10 atoms of HYDROGEN
2 atoms of OXYGEN
ON THE RIGHT SIDE of the equation we have:
2 atoms of HYDROGEN
1 atom of CARBON
3 atoms of OXYGEN
I'll start by balancing CARBON on BOTH sides of the equation:
C4H10 + O2 => H2O + 4CO2
**so now we have 4 CARBON atoms on both sides, but have 2 atoms of OXYGEN on the LEFT and 9 OXYGEN on the RIGHT
Balancing the OXYGEN on BOTH sides:
C4H10 + (9/2)O2 => H2O + 4CO2
**so now on the LEFT we have 9 OXYGEN (because 9/2 X 2 = 9) and on the RIGHT we have 9 OXYGEN (1 + 8 = 9)
now we have to balance the HYDROGEN on both side:
C4H10 + (9/2)O2 =>
5H2O + 4CO2
**so now we have 10 HYDROGEN on each side. But we have a problem, on the RIGHT we have 13 OXYGEN on the RIGHT side and on the LEFT we have 9 OXYGEN.
this next step is really important: DON'T FREAK OUT!
Adding 13 OXYGEN to the LEFT:
C4H10 + (13/2)O2 =>
5H2O + 4CO2
So now we look at our equation:
LEFT SIDE: 4 CARBON, 10 HYDROGEN, 13 OXYGEN
RIGHT SIDE: 4 CARBON, 10 HYDROGEN (5 x 2 = 10), 13 OXYGEN (5 + ((4 x 2)) = 13)
So the law of conservation of mass is satisfied.
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