English schools
English schools in Ireland are regulated by law. Make sure the school in which you plan to enrol is recognised by ACELS.
More information can be found here.
Residence permit
You don't need a residence permit for short courses (up to three months). However you might need an entry visa depending on your citizenship.
You can enrol on a longer English course. In such a case, you'll get a residence permit for 8 months, which typically includes 6 months of classes and 2 months of vacations. With this residence permit you can legally work in Ireland part-time (20 hours per week) or full-time, depending on whether you attend classes or not.
Accommodation
There's a serious housing crisis in Ireland, especially in Dublin. The demand is high and rents are expensive. Most students share an apartment or house with other students.
There's also a lot of scam so be careful. You can find accommodation on Daft. Never send money before a viewing and make sure to check the landlord's ID before signing a contract.
There's a mobile app for rental ads, Dublin Expats (iOS, Android), which verifies users' accounts (by checking their passport) to make the property rental process safer.