There is a fair bit of precedent, though none of it is very recent. The provisions are found not in Universi Dominici Gregis itself, but in the companion book of ritual, Ordo rituum conclavis (see UDG §90). This 2005 edition is the latest in a series first codified in 1516 and frequently republished.1 I do not know if the 2005 version makes any changes to this rule, but if it did, it would be the first since 1516.
The procedure is actually quite simple. Ultimately, the person chosen has to accept or refuse his election, and so either he has to come to the college, or they have to go to him.
If the person chosen is in or near Rome, then he is summoned to the conclave, and asked if he accepts the election. If it's a yes, then he becomes Pope; otherwise, he doesn't, and the cardinals go on to elect someone else. A notable example of this process - and the most recent example of a non-cardinal being chosen - was the election of Urban VI in 1378. In order to preserve secrecy, the conclave summoned several decoy clerics at the same time.
If he is further away (the text says aliquos dies - a few days' travel) then the election is announced and the conclave breaks up. They draw up documents certifying the election, and send a delegation of cardinals to the person they've chosen. If he accepts, then he becomes Pope, and they all go to Rome for the rest of the usual ceremony. Otherwise, the delegation would return alone, and the conclave would resume - but this has never happened. An example is the election of Gregory X in 1271, who was off crusading with Edward I of England.
In modern times, the second process is quite unlikely to happen. The most plausible candidates for Pope who would not already be in the conclave are (1) cardinals above the age of 80, like Francis Arinze, who might well be in Rome anyway, and (2) bishops of important sees, who would tend to live in major cities that are well-connected to Rome by air travel. But there is no strict dividing line: it's up to the cardinals to decide which procedure would work best in the given circumstances (UDG §5).
The person elected is told why they are being summoned - although it wouldn't be too hard for them to guess. They can't tell anyone else, though! (I don't know if the decoys in 1378 knew they were decoys, or if they had a disappointing surprise.) There is no oath provided, unlike for the electors or their assistants, but if there were any doubt about whether secrecy was required, UDG §5 or Secreta continere (1974) §§7, 10 would seem to give ample scope for imposing it.
Speculation: In the same way, if the cardinals felt it necessary, they could arrange for dummy smoke signals to be sent out. (The white smoke / black smoke system is not prescribed in law: although the ballots must be burned, there's nothing to say what colour the smoke should be.) This would disguise the fact that balloting was not taking place, while they were waiting for the chosen person to arrive, and so the world's media wouldn't be encouraged to start scouring the area, hanging around Da Vinci airport, etc., in the hopes of finding out who had been summoned; and the waiting crowds wouldn't be misled into thinking that the new Pope was going to appear on the balcony quite soon.
1. The 1516 book Rituum ecclesiasticorum sive sacrarum caeremoniarum Sanctae Romanae Ecclesiae contains provisions on Papal election and coronation, from the work of Agostino Patrizi Piccolomini (1435-1495), who was Master of Apostolic Ceremonies and Bishop of Pienza. He drew on less systematic accounts from as early as the seventh century.