How long does it take for togepi to evolve

Togepi's evolution is friendship based.

Here are some tips:

Friendship:
This is easily one of the trickiest means for a Pokemon to evolve as it’s very hard to gauge, even with the Poketech Application. Still, it’s possible with some time and some knowledge. If possible, try to catch the Pokemon with a Luxury Ball is it makes it easier to raise happiness. Once something is happy enough, the time it levels, it will evolve, provided there aren’t any more requirements. The most standard ways to gain happiness in Pokemon would be:
1) Having it in your Party: They love being used in battle and they like being with you.
2) Drinks from Veilstone Department Store (Lemonade, Soda, Water in that order)
3) Poffins (their favorite kind)
4) Winning Super Contest
5) Veilstone and Ribbon Syndicate Massages. Veilstone has the advantage of getting an accessory as well.
6) Vitamins: From the Veilstone Dept. Store, while only 51 can be used, it’s a great way to raise something simply because
7) Berries: Specifically the EV Reducing berries, a great way.
8) Amity Square: Open to only specific Pokemon, it’s still a good way to raise their happiness. It is important to check on them every 200 steps to see if they have picked up an item.
9) Soothe Bell: Slow but reliable. Recommended with a Luxury Ball

The quickest way of raising a Pokemon’s happiness is also the one that should be done the soonest. The most efficient way I’ve found is to use the EV Reducing berries: Pomeg, Kelpsy, Qualot, Hondew, Grepa and Tamato. While this is a very efficient method, about 35 berries, it isn’t without risk as it reduces Statistics if Effort Values are figured in. It’s a lot easier to have something hold an Everstone to learn moves than to struggle through happiness-gain more than needed

I'd suggest reading the following guides:

Pokemon Evolution 200

Pokemon Platinum Happiness Guide

Have fun evolving your pokemon!