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You can either get explorers as preprogrammed events or as random events. There's nothing you can DO to get them, you can just sit and hope that some gifted madman will be born in one of your provinces.
If you are determined to alter the course of history then you can always look carefully at a save game file and edit it to give yourself a leader at the appropriate time. I confess I have done this to extend the lifespan of a leader before. I figure he would not have been included in the history books if he died before he got a chance to explore something. Playing minor states you will need to do something unless you are prepared to play in the hope that a random event gives you a break. The advantage of random leaders is that they are immortal (currently) so unless they die in battle you don't have to worry about them expiring before they get to uncharted territory.
Explorers are special admirals. So they are never found walking over the country but always attached to ships. You´ll be informed if one will be available at the beginning of a year (usually with three ships already in a port). A fleet with an explorer can sail into 'mare incognita'. When sailing along a shore there´s also a chance that the provinces bordering the coast are unveiled. They also lessen the attrition effect on the fleet. Terra incognita on the other hand is to be explored with conquistadors. You´ll also be informed if one is available (in a city). If You have reached a certain landtechlevel (13 I think, but I always tend to forget these things) You can explore the land with any army. Same goes for navy (can´t remember the needed level also at the moment). You can load an army with a conquistador on a fleet with an explorer-admiral and so combine both efforts. Exploring a shore and then unloading the conquistador with his army.
Leaders will have a sextant symbol beside their name if they are naval explorers and a copper helmet symbol if they are land conquistadors. If you don't get any of these, your only hope is land tech 11 and naval tech 21 to allow regular troops to explore.