It is unlikely that you are going to be able to get an attorney to take a case on a "pro bono" basis (for free). Keep in mind, when you are asking a law firm to take on a case "pro bono" you are asking not only that the attorney donate their time to your case (time that could be spent generating work for clients that are paying for his or her services), but you are also asking that the law firm actually spend a fair amount of their money to litigate your case (it costs law firms a lot of money to litigate something for their clients (costs of filing fees, staff expenses, copying, subscriptions to legal research and other software, etc.), so there are not many firms that can provide pro bono litigation services.
You can check with firms (usually look for larger firms that can absorb these kinds of economic losses), and see if you have something in your case that offers them a good trade off. (Is your case noteworthy or somehow able to generate some news for the law firm - pro bono representation can be a form of very inefficient advertising, but if your case can get their name out there, it may be worthwhile; Is your case a cutting edge matter - some law firms and attorneys are interested in being the first attorney (or one of the first) to litigate a big issue, they want to argue an issue before the appellate courts that may make new law; Along the same lines, does your case have an issue that compliments or is similar to the firm's other (paying) client's interests - for example, if you have a land use issue for a small property, and the law firm represents a lot of big property owners with similar interests, that may have the same issue, the law firm may be willing to represent you in order to resolve this particular issue).
An alternative type of representation (that is more commonly used when the client does not have a lot of funds) is the "contingency fee agreement" where the law firm will advance its services and the costs of litigation, in exchange for a portion of the client's recovery. So the client will get representation without having to pay anything up front, but will have to reimburse the law firm for its expenses, then pay the law firm a portion of their recovery to compensate them for their time and efforts. (These fee agreements can be changed between the parties, and some lawyers will have the client pay for the litigation costs as the matter is being litigated, and the client will only have to split part of their recovery to pay for the attorney's time when they win).
It is important to discuss with your attorney the details of your compensation agreement at the time that you sign up for services (this contract is usually referred to as the "Legal Services Agreement"), and if you have any questions, the lawyer should be more than willing to explain and discuss them with you.
Some attorneys do donate their time to good or noteworthy causes (defense of children's rights, for example), so you can always ask.
You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).