At its core, a breach of contract claim says that one party agreed to do (or not do) something but failed to perform as agreed. Let's reverse engineer that core proposition.
1) Valid contract
For parties to have agreed, then, there would have to have been an agreement. In addition, that agreement must have constituted a valid contract. (As you will see shortly, courts tend to reference the "valid contract" element first. The reason we don't do that here--that is, yet, at least--is that we're first working backwards from what we said above to be the core of a breach of contract claim.)
Circling back to that first part, now, the whole of stating that "we had an agreement" is to establish the part of that agreement at issue. That is, what did the breaching party not do that they were obligated to do (or do that they were obligated to not do)? That is usually the second element D.C. courts reference.
The act of the breaching party not doing something they were obligated to do (or doing something they were obligated to not do) is usually the third element D.C. courts reference.
How was the non-breaching party harmed by the breaching party's breach? Those are the damages, and D.C. courts tend to reference this element last.
In Zaccari v. Apprio, Inc., the court wrote that:
Under District of Columbia law, to prevail on a claim of breach of contract, a party must establish (1) a valid contract between the parties; (2) an obligation or duty arising out of the contract; (3) a breach of that duty; and (4) damages caused by breach.
Since there is not much "legalese" obscuring the plain-meaning of those four elements as written by the court, the requirements set forth in Zaccari should be simple to at least understand--even if you're not a lawyer.
Other nuances to be aware of before beginning your breach of contract claim
First, you need to calculate your damages, and you need to let the breaching party know what you've calculated your damages to be; any damages about which you did not apprise the breaching party before initiating your lawsuit may not be recoverable; so, this is important to remember and do!
Second, for a party to bring a breach of contract claim, that party cannot have previously breached the contract. So, you need to be prepared to show that you performed as agreed, while the breaching party did not.
Third, some contracts specifically require that the non-breaching party give the breaching party notice of the breach. This gives the breaching party a chance to "cure" the breach (and, among other upsides, potentially spares judicial resources from having to address your matter). In general, the law in Washington, DC favors this extra requirement of prior notice. So, to be safe, you should also be prepared to show that you let the breaching party know about their breach prior to you filing the lawsuit.
Lastly, there are different "levels" of contract breaches: major ones and minor ones. In contract parlance, these are referred to "material breaches" and "non-material breaches" respectively. If you think about a contract as something that contains a core set of obligations and an ancillary set of obligations surrounding that core, then we might describe non-material breaches as an issue pertaining to one of those ancillary obligations (examples: expectations of professionalism, service quality, or the use of certain procedures during performance of the contract). On the other hand, a material breach is more serious because it deals with non-performance of one or more of those core obligations (examples: failure to perform the contracted-for service in full or failing to deliver purchased goods). In many cases, defendants want to characterize breaches that you consider to be major to be only minor, for obvious reasons. But, other than preparing your arguments and evidence in advance, you need not spend too much time debating this with the defendant on the side: the judge, or jury, will decide, if the case goes to trial.