It sounds like there is a new folio registered to the original vendor on foot of an application for first registration. Now that this is completed, the original vendor can transfer this title. (I would have handled it differently - allowing buyer to take over the job of registering the title, but that is somewhat academic now and the parties may have had their reasons for doing it the way it was done.)
If matters are as set out above, then the deed of transfer has to be prepared, stamped by Revenue ( presumably exempt from Stamp Duty if price is nominal - but still needs to be stamped) and registered in the Land Registry. Some ancillary documents will also be required.
This is relatively straightforward, but it is really a new, stand-alone transaction from a solicitor's perspective. As such, it would still attract a legal fee of perhaps €300-€600 plus VAT @21.5% and outlays ( circa €150-€200). And depending on the circumstances, solicitor might insist on both sides having independent legal advice.
I concur with MF1 on wisdom of transferee doing the work him\her self