Depending on how you set up the company, it can be reasonably easy or reasonably difficult to do what you are doing.
If your company is registed as a single-member company (one shareholder), you need to convert the status to a 'multi-member' company. Unless you do this, any shares issued to another person are worthless. The conversion is reasonably simple, just a form to be signed, should be able to download from CRO
Assuming this is done, you can look at 'transferring shares' or issuing shares. If you want to split the share capital with another person as you seem to be intending, I think you are better off issuing this person with 2 new shares (so you each have 2 shares), rather than transferring 1 share.
I got my accountant to do this, and was completed very quickly with only a few things to sign.
Andrew