If you decided to issue a claim, you would then need to register at this site: http://www.moneyclaim.gov.uk/web/mcol/welcome so that you are ready to issue the claim in the event they dispute the claim and do not pay you.
The website is very user-friendly and you would not need a lawyer to use the money claim site. Claims with a value of under £10,000 are classed as a "small claim", so legal costs are generally not recoverable and the matter may be dealt with on paper by a Judge, not at a hearing. This means the parties are on an equal footing, so you don’t need to worry about legal costs if you lost.
A hearing may be necessary if the court thinks that oral evidence is required to dispose of the case. The court will then issue the claim and they will send you "notice of issue". The papers are served on the defendant who then has 14 days to acknowledge the claim - they do this by filling out an acknowledgment of service and they post it to the court.
They indicate their intention when they do this, i.e. whether they admit the claim in full or partly, or if they deny the claim. If they want to defend the claim then their defence is due by 28 days from the date the court served them with the papers.
The central court processing centre then sends the claim to the defendant's home county court for case management and directions - the directions will give a list of dates which you both must comply with.
The court should offer you mediation to encourage you to resolve the dispute early on - though for mediation to work both parties have to agree to participate.
If there is no settlement then the claim will be dealt with at a final hearing which takes anything from 9 to 12 months from when you start the claim - longer if the claim is of higher value. You can pursue the claim yourself or use a law firm.
For the hearing you can use an advocate if you wish, though it's not compulsory. I have details of law firms and advocacy agencies if you would like those. Though in a small claim you won't be able to recover their charges from your opponent. A small claims hearing is easy to deals with- it's quite informal and no lawyer is required.