You can follow precisely what is happening in the institutions - Parliament, Council and Commission, through their websites. You can find them all at: http://www.europa.eu.
And the Parliament and Commission have offices in Dublin designed to provide information about what they are doing. The Council does not have a separate office in Ireland as it is made up of the member states' governments, and so its Irish representative is the Oireachtas.
The most personal contact is through your local member of the European Parliament. To accommodate the new member states after the elections this June, Ireland will have 12 MEPs in total, down from 13. Three MEPs will represent each of the four constituencies. Many of them hold regular clinics and are contactable through their offices in their constituencies and in Brussels. See: http://www.europarl.ie/irish.html
Your MEP may be on one of the committees considering a particular piece of legislation where they can represent your views. They can also do this through the group they belong to in the Parliament and through their contacts with other MEPs.
All legislation when drawn up by the European Commission goes to the Oireachtas and to the government. The Taoiseach and the ministers agree their position on the draft laws and the Irish civil servants in Brussels meet the civil servants from the other member states in committees to thrash out the details.
The European Affairs Committee in the Dáil considers all such legislation also before the government finally signs up to it. You can find their members and reports at: http://www.oireachtas.ie
Contacting your local TDs and Senators or going straight to the relevant Minister is the best way to influence the government.
You can be involved in legislation right from the beginning, from the time the Taoiseach and other member state leaders request it or the Commission instigates it.
To find out what the Commission is doing of direct relevance to Ireland, go to: http://ec.europa.eu/ireland/press_office/index_en.htm
The Commission, responsible for drawing up the draft laws, frequently holds consultations with interested people and bodies through the internet. To find out what they are currently consulting about and to make your voice heard go to: http://ec.europa.eu/yourvoice/index_en.htm
Here too you can send your opinion, read blogs from others, take part in forum discussions, give your feedback, discover your rights as an EU citizen and where to go to for advice. You can even discover what your fellow EU citizens in other countries feel about a host of issues through the results of opinion polls on Eurobarometer.
The Commission makes public many of the submissions it receives, and these can be read on-line. They publish the results of the consultations and the draft legislation when it has been compiled.
Every big organisation and interest group from farmers to pharmaceuticals, trade unions and employers bodies, accountants and anti-poverty groups has a representative body in Brussels. They lobby on behalf of their members and can be found through a web search or through your local organisation.
You can highlight a problem that you believe the government is not taking enough notice of through the petitions committee of the European Parliament. They don't have the power to put it right, but those involved including the Commission will be asked to attend a public hearing in Brussels when your case will get a thorough airing designed to shame the culprit to put things right.
Your local MEP will help here and you can get more information on the website: http://www.europarl.europa.eu/parliament/public/staticDisplay.do?id=49
When you have a complaint against any of the EU institutions or bodies you can take it to the Ombudsman and do so in any of the official languages including Irish.
Details of how to contact him and the national ombudsmen are found at: www.ombudsman.europa.eu
There also you will find details of other help available to you. One such trouble-shooter is the European Consumer Centres Network (ECC-Net) that helps consumers with cross border disputes. This is useful for instance for people who buy from websites in other EU countries, or when on holidays and have problems later. http://www.eccdublin.ie/
Then there is FIN-NET for settling cross-border financial disputes out of court and SOLVIT, an online problem-solving network for citizens who are victims of public authorities not applying single market rules properly. An example of this would be non-recognition of professional qualifications in another country or market access of products.
There is the ADR - Alternative Dispute Resolution - that is an alternative to legal actions and the ECC-Net can advise you about them.
There are various citizens groups also that aim to influence what the Union does. One of these is The European Citizens' Consultations 2009 that include NGOs, universities and think-tanks from all the member states.
They are to be found at http://www.european-citizens-consultations.eu