The most common way a home is given an approximate value is a Comparative Market Analysis (CMA).
Most real estate agents will do a CMA as a free service for any prospective client. The CMA is determined by pulling comparable properties in your general area that have sold in the past 4-6 months. The properties are assessed for selling price, time on the market, improvements, square footage, and other variations that are then used to give an approximate value of your home.
Because real estate markets change rapidly, a CMA can be out of date in a few months in some markets. It is always important to have a current CMA when considering the sell of your home.
CMAs, while based on data, are still very subjective. When looking at comparable properties it may be hard to account for things such as curb appeal, desirability of the home's architectural style, etc. This is where the agent's experience can help you.
It is vital that you first find a good agent, and second, that you take their advice when they give you an estimated value on your home. Agents are not emotionally or personally attached to your home. You, as the owner and occupier of the home for years, are most certainly! If you watched your kids grow up in the home, celebrated birthdays there, had family gatherings, and painted the walls bird-egg blue 10 years ago, you definitely have value in this home that cannot be expressed in dollars.
That value, while priceless to you, has no worth to a prospective buyer. That is why you should never attempt to price your own home. Let someone who has no attachment to your property take on this task. That is, unless you want the home to sit and languish on the market for much longer than necessary.