When applying for a home equity loan, there are 3 main things that lenders look at:
1) Your credit history
2) Your income
3) The loan-to-value ratio of your house
 
Applying for a home equity loan is much like applying for a regular mortgage.  Some fees that may be associated with the loan are:
-Application fee
-Appraisal of property fee
-Title search fee
-Fee for preparation of the documents
-Interest
 
Some fees that may be associated with the line of credit are:
-Charges for maintenance
-Transaction fees
-Fees for inactivity
-Interest
 
Other things to check out when applying for a home equity loan:
1) Is there a prepayment penalty?
2) What kind of rates are other financial institutions offering?
3) Are other lenders charging less in fees?
3) What kind of deductions can you expect from your loan?
 
Other things to consider when applying for a home equity line of credit:
1) What is the index rate?
2) What is the margin added to the index by the lender?
3) What are the caps as to the amount and frequency that the interest rate can change in a given year?
4) Is there a minimum monthly payment?

Related Articles:

What Exactly is Home Equity?

How Does a Home Equity Loan Work?

Home Equity Lines of Credit

Understanding Your Credit Score