Acid-base reactions are an important part of any chemistry class, and understanding the mechanisms behind these reactions will serve you well from general chemistry all the way through biochemistry.
When you are presented with two reactants and asked to predict the product, it's normal to be intimidated and even lost at first - but if you can remember what to look for, you'll be able to sort out any reaction quickly.
Lewis bases donate an electron pair, and the acid accepts. Acids and bases can fit either one or both definitions, and you can determine which by drawing the molecule and looking at the mechanism.
The strength of an acid or base is determined by how willing it is to perform the role. If a molecule is desperate to give up a proton, it's a very strong acid. If it's holding very tight to its electrons, it's a strong base.
For instance, consider propanol. Draw the molecule, including all the hydrogens. Use a structural formula rather than bond-line, because it's easier to see what's going on when all atoms are labeled. You immediately see a hydrogen atom attached to the oxygen - so draw the molecule again with charges, but leave the hydrogen off. This is the conjugate base.
You'll notice it's stable because the negative charge is being absorbed by the electronegative oxygen atom. Because all molecules strive for stability, this means that propanol is very willing to give up this hydrogen, making it a strong acid.
When analyzing the stability of a conjugate, there are four factors to consider. The first and most important factor is which atom carries the negative charge. If it's a very electronegative atom, it's stable. If it's less electronegative, it's less stable. Sometimes, you'll have to compare the relative acidity of two different protons on the same molecule.
What happens when they're both on the same kind of atom? Obviously, the atom isn't the deciding factor - so look at resonance. Resonance helps spread the negative charge over a larger area of the molecule, making it more stable. If resonance isn't a factor, look for induction.
If there's a very electronegative atom within one bond or so of the charged atom, that atom pulls the rest of the molecule's electrons slightly toward it. This effect is called induction which helps stabilize a negative charge.
If there's no induction, look for double or triple bonds - multiple bonds are areas of electron density, and will also help stabilize the charge.
Drawing the mechanism of the reaction will help you predict the products. Draw the two reactants, and look for signs of electron movement. If you see an electron-rich area on one reactant, look for an available proton on the other reactant.
Draw a curved arrow from the electron to the proton, then from the proton's bond back to the attached atom. Don't break the octet rule. By following the arrows, the structure of your product will become clear.
This is a very simplified version of an acid-base mechanism, but it gives you a basic idea of how to approach these types of problems. Like anything else in chemistry, the only thing that will help you master the subject is plenty of practice.