Before doing anything, ask yourself if you can settle the dispute. The other person or company may be amenable to negotiation. That way you avoid court courts and legal fees.
If you can't work it out, then you might decide to hire a lawyer and go to court. If the dispute is for a small amount of money, it might be better to represent yourself. Each state has the equivalent of city court, small claims, minor disputes and major ones. You need to know what the dollar sum is before you select a court.
The larger the dispute or the more complicated it is, and the more sense it makes to hire a lawyer. Remember hiring a lawyer means you pay the legal fees and costs of experts. The other side is rarely ordered to pay your expenses in litigation.
Lawyer or Not
Selecting a lawyer familiar with commercial litigation is a formidable task. You can check with other businesses about who they use; you can also check with the county bar association to find out what lawyers in your local area do commercial litigation. For some disputes it is far less expensive to do it yourself. Other matters require a lawyer. Some states will not permit corporate entitites to represent themselves pro se.
Federal or State Court
If your target is from another state, you have to decide if you will sue in that person's state or in your own, or in federal court. Federal court requires diversity of citizenship (all of the parties must be from different states) and that the dispute exceeds $150,000. Your own state may be the easiest for you, but collection action in another state are sometimes easier if you have local court orders and a local attorney helping you. In some cases you might want a home state lawyer and an out of state one.
What is the argument about?
The most common business argument is breach of contract. Someone failed to follow through on a promise. It could be as simple as not paying a bill, or it could be poor workmanship, or even misrepresentation of what someone's goods or service can do for you. In many states, unless fraud is involved, such business disputes are done before a judge only court (no jury). Disputes can also be two sided, one party may claim they were cheated, and the other party make the same charge. For example, a supplier may demand $20,000 for a delivery while the recipient counterclaims that the product was shoddy and cost them loss of customers, etc.
What has to be done?
Your lawyer will need to see the relevant documents, such as contracts or proposals. The most difficult suits to litigate are those where the parties have an "oral" agreement and expect the court to enforce it, and the two parties have completely different recollections of what was promised. Court procedure normally includes an exchange of written questions and answers (interrogatories) and depositions (question and answer sessions before a court reporter --the questions are asked by the attorney for the other side, and then the attorney for the witness may ask cross questions ). Then the matter may go to arbitration and/or mediation to avoid a trial.
Mediation or Arbitration
These are procedures where another lawyer or business person works together with the parties to resolve the issue. They can go for many days or be over in an hour. Some courts mandate them, sometimes parties prefer them, and sometime they succeed. If they do not, then the matter goes to court.
Complicated matters require experts for both sides. For example, a breach of contract involving the wholesale purchase of tools, might be easily resolved without an expert. The plaintiff shipped 200 boxes of tools which costs $100 per box and is owed $20,000. The plaintiff has the proposal, the shipping order and proof of delivery. Obviously anyone can see that no expert is needed for such a dispute. Others might be much more complicated. For example, the plaintiff provides a very sophisticated software program which has been granted an exclusive patent, and the dispute is about reverse engineering, i.e., "stealing" the idea without paying a license and/or users fee. Such an argument would require an expert in the field of patent law, software programming and reverse engineering. A judge might want this dispute to be argued before the bench (judge only) or a jury. This usually means an exchange of written opinions from the experts and expert depositions before trial.
The matter goes to a judge only court or a judge with a jury. The plaintiff presents the fact witnesses and experts. The defense does the same. Either the judge or the jury deliberates and then the court issues a verdict. Verdicts can be 100% for the plaintiff, a split decision or no cause (which is a defense verdict). Lawyers can shepherd their clients through the pretrial and trial time. No lawyer can ever guarantee what a judge or jury will decide. The lawyer's job is to advocate your position and present your arguments and be as persuasive as possible. The other side has their lawyer doing the same thing. Some disputes are so clear that the jury grants a verdict 100% for the plaintiff, others are more murky and lead to a split. If the jury cannot decide, the matter may be no-caused, or a mistrial called, which means the parties need to go to another trial. Sometimes the costs of another trial will lead some parties to settle.
If a jury awards a verdict, the other side can accept it and pay it. The losing party is allowed to appeal to a higher court if they believe there were errors in the trial. Sometimes the defendant does not have the resources to pay the verdict, and then the winner has to follow a collection action. Verdicts can be filed in the state court office and becomes a financial lien on any asset owned by the loser. Sometimes a loser will go into bankruptcy to avoid paying a judgment.