Most agents will perform a free Comparative Market Analysis (CMA) which will provide you with an estimate of your home's value on the market. This is a free service that agents provide in the hopes that you'll utilize their services as a sales listing agent. The CMA is done by comparing the location, size, features, and condition of your home to other properties in your area that are currently on the market, or that have recently sold. It's generally best to use an agent that lives, works, or specializes in your area since they will be familiar with the sales history and will have presumably visited many of the other homes currently on the market to provide you with the best estimate.
As for a free appraisal, an appraisal is usually performed by an appraiser that is hired by the bank underwriting the mortgage. The appraisal value will be used to determine the maximum mortgage amount that the bank is willing to finance on the property being sold/purchased. This is a step where some contracts may fall apart since often times there will be language in the purchase contract that stipulates the agreed purchase amount is contingent on mortgage financing. If the appraiser values the property at or above the purchase amount, the contract fulfills the mortgage contingency, otherwise if the appraisal value falls below that amount the contract may be void.
Appraisers get paid, usually by banks, who then usually charge the borrower/buyer of the mortgage the cost which will go into the closing costs. Banks writing mortgages generally do not accept any other appraisal report other than the one they paid for, so it is not to your advantage to get a free or paid appraisal separately from the bank.
I live in Somerville and right now there is an extreme shortage of properties on the market with an abundance of buyers making for a great seller's market. If you have any other questions, feel free to ask or contact a local agent.