There should be plenty of info on sites such as myhome.ie or also alot of the banks have good online buyer guides.
With private treaty the steps generally are:
1. figure out your budget, i.e. what can you afford. Good idea to get approval in principle from a mortgage provider at this stage. Might be worth looking for a solicitor & surveyor also.
2. view house.
3. make offer to vendor via the estate agent. this is usually verbal.
4. some too-ing and fro-ing. Offer is accepted.
5. You then usually have to put the offer in writing (make it subject to a survey/snag) and pay a deposit of a few €K. This is refundable.
6. You give them the name of your solicitor. You arrange a survey. You apply for your mortgage.
7. A few weeks pass, assuming the above goes ok contracts are ready to be signed. This is the point of no return!!! up to this either party can back out. A further deposit is usually paid at this stage, bringing the total to 10%
8. As part of 7. a closing date is agreed, this is when the keys will be handed over and the mortgage be drawn down. Unfortunately the seller can sometimes delay this and cause problems.
9. closing date arrives, your bank sends the check to your solitictor who gives it to the seller's solicitor. You get the keys and move in!