Cloning in Pearl is actually quite hard, definately more so than it was in Silver.
For this example, let's use an Empoleon.
Go to the GTS building in Jubilife city with Empoleon in your party. Log on to GTS and offer him for trade. Just remember that people can actually take it if they have the trade you ask for, so choose carefully. I always go for level 100 female Bonslys, because there can't be many of them around and I would actually be happy if one showed up!
While Empoleon is being uploaded to the GTS, you then have to turn off your DS at the exact right time.
Turn the game back on IMMEDIATELY. One of three things will happen:
1, You get a blue screen saying 'the save file was corrupted'. Empoleon is still in your party. When you log back on to the GTS, it asks you to 'Deposit Pokemon'. You turned off the DS too early, and nothing has happened.
2. You get a blue screen saying 'the save file was corrupted'. Empoleon is still in your party. When you log back on to the GTS, you see 'Summary'. A second Empoleon awaits, hooray!
3. The game starts without a blue screen. Empoleon is not in your party. You turned off the DS too late, so Empoleon has been uploaded to the GTS without cloning. You should immediately take him back.
Getting the timing right is very hard. All you've got to go on is the little clock that rotates in the bottom right corner on the 'communicating...' screen, and the WLAN lights on your modem that flash when the DS is using wifi.
For me: Somewhere between 7 and 9 rotations of the little clock, the light on my modem will flash exactly ten times. I need to turn it off around the fourth or fifth flash. This is *just* before the animation showing my Empoleon being uploaded would normally start.
You're going to have to upload a bunch of mon and watch the little clock and your modem lights until you know exactly what works for you. It's taken me a few days to get it to work even 50/50.