As BrenG mentioned above, in a single member company, the membership refers to shareholders (or owners) of a company. So whilst it is possible to have just one shareholder, its is still a legal requirement to have a minimum of two company directors. Directors are the inidividuals responsible for the day to day running of the company and ensuring compliance while the shareholders are the actual owners of the company. In small companies, 99% of the time the shareholders and directors are the same people.
In relation to setting up the company, it is best going to a company formation agent to do so. The main reason being is that they can usually register your company in 3-5 working days. While going to an accountant to do so is also a good idea, in my experience a lot of accountants outsource formation agents anyway to set up the companies for them (because formation agents can do it faster).
In relation to the link above for formacompany.ie, while €75+vat for a company formation sounds cheap, it was more of a headache for me than anything else. Although they will draft the paperwork for you, you have to file the documentation with the Companies Office yourself and pay the filing fee to CRO of €100. By submitting your company manually, as i did, it will then take from 4-5 weeks to have your company registered. After that you will need to purchase a company seal, and perhaps a company register also which will cost you approx €50. So for €225 (€75+€100+€50) it will take you 5 weeks to set up your company with this crowd and you have to do most of the work yourself.... Some company formation agents do all this work for you in 3-5 days including filing fee's and company seals etc for approx €252... I'd say it'd be worth your while spending the extra €27!!!!