Once a dispute cannot be resolved by a conversation, there is a choice about how to resolve it — and the default assumption of "we'll see them in court" is usually the most expensive option available.
Negotiation, properly
Most disputes are settled by the parties, and the ones that settle early settle better. What makes it work is preparation rather than goodwill: knowing what you would accept, what you would refuse, and what happens to you if there is no agreement at all.
That last number is the important one. If the realistic alternative to settling is eighteen months and substantial fees, a settlement that felt disappointing may be the better outcome, and knowing that before the conversation stops you rejecting it out of pride.
Mediation
A neutral third party helps both sides reach agreement. They do not decide anything — they manage the conversation, test each side's position privately, and look for a landing point.
It is quick, comparatively cheap, private, and it does not damage the commercial relationship the way litigation does. It works well where both parties want a resolution and are stuck on how, and badly where one side simply has no intention of paying.
An agreement reached in mediation can usually be made binding, which is worth doing — an understanding that is not written down and signed is not a resolution.
Arbitration
A private process where an arbitrator decides, and the decision binds. Faster and more private than court, and it can be expensive, since you are paying for the arbitrator as well as your own representation.
Check your contracts. Many commercial agreements contain an arbitration clause, in which case the route may already be decided and going to court instead is not available to you.
Court
Appropriate where the amount justifies it, where the other side will not engage at all, or where you need something only a court can give.
Go in knowing the cost, the timeline and the realistic prospect of recovery, and get those from an attorney in writing before starting rather than discovering them along the way. Legal claims also expire after a period, so a matter left indefinitely may cease to be actionable at all.
The question to ask first
What do you actually want? Payment, a completed job, an apology, a supplier relationship preserved, or simply to stop thinking about it?
Those have different best routes, and businesses regularly spend heavily through a process that was never going to deliver the thing they actually wanted. Being honest about the answer is the cheapest step in the whole exercise.
General guidance, not legal advice. Prescription periods, arbitration clauses and costs are consequential; take proper advice before committing to a route.