There are a great deal of commonly misunderstood facts regarding credit repair and scoring. In fact, the calculations that credit agencies use are closely guarded secrets that can only be estimated. In relation to your question, the answer is not as simple as the question.
There are three major credit rating agencies and each has its own formulas - this is why each consumer has three different scores. Also, scoring is largely based on what is reported by creditors, therefore, paying off a bill may have a delayed impact or no impact at all - it all depends on the creditor and type of credit. In addition, the type of "bill" you pay off affects your credit differently, revolving credit has a greater impacted than structured debt, and closing an account after you pay off the bill may actually have a negative impact on your score.
If you are planning to buy a house, you want to achieve a minimum score of 620 to qualify for a mortgage loan under current market conditions. There are several very affordable credit repair firms that can assist you in this effort without it being reflected on your credit report. If you would like a reference, let me know and it will be my pleasure to help.
My best to you on your journey!
Patrick is correct that the exact methods of each agency vary. I believe in part it will depend on the size of the debt you pay off, your remaining debt and keeping the account open.
It used to be taught that old accounts should be closed, but this actually lowers your score. One method of improving your score is to increase your available credit. While getting debt free is a great goal, if you hope to increase your score, once you pay one debt down to 1/3 of its high credit limit, shift your focus to other debts to reduce them to 1/3rd as well. This will gain you the most points the fastest.
If you are in a great hurry, ask your lender about Rapid Rescore as you make progress paying down your debts. It's legal and for a fee can give you an upgrade in days rather than months.