Put in your offer, ignoring what the estate agent told you. You will quickly receive feedback on it. If its rejected you will have to decide how much higher you will go.
The main pointis that once you place an offer the agent will have your contact details and will update you on any counter bids.
If you do get the house, you will be asked to pay a deposit to secure it, approx €5k to €10k, you pay this by cheque to the estate agent. At this point the house is marked 'Sale Agreed'. You should then engage your surveyor, lawyer etc.