I always mess up with my writing by adding commas and full stops (periods) in the wrong places. Is there any rule of thumb or some other way that I can follow to avoid this problem?
ElendilTheTall has great advice regarding placing commas when you pause when reading a sentence aloud. The only thing I feel needs to be added to that answer is to not overuse commas; that is, don't use a comma when you need a period.
Each sentence sentence normally should not have two main clauses separated by a mere comma. For example:
This is incorrect, because there's two distinct thoughts and two verbs here ("I love" and "I buy"). The correct version would be:
Alternatively, since these two thoughts are closely related you could use a semicolon instead of a period:
Note how in this case you would not capitalize the letter after the semicolon, because it is not the first letter of a new sentence.
EDIT 2: User psmears pointed out another error in my explanation; my explanation was too simplistic and excluded some perfectly acceptable sentences. You can join two main clauses with a coordinating conjunction. User psmears gives the example,
In this case there's two clear main clauses, each with their own finite verb ("like" and "hate"). However, while this is perfectly acceptable for short, closely relayed clauses, it can quickly lead to run-ons if you're not careful:
Write a sentence, then read it back to yourself. If at any point you feel the need to pause, that's where you put a comma. Once you have practiced like this for a while, you will be able to put them in as you write.
Full stops go only at the end of sentences; it's that simple.