Some rats litter train easily, ans some don't. Some go in one corner all of the time, Some don't. Mine are part of those that don't fit into the normal rat category. Just in case yours ends up in the same category, I'll go ahead and let you know what I have done.
My rats poo whenever the feeling hits them. If that means they are in the middle of a bound over the couch, so be it. Out it flies. They have since stopped using the couch as a pooing area, but that was the first few months I had them. Now they poo in the cage while doing whatever. There is no "poo stance" that I can find. Some individuals can tell when theirs are ready to go. Mine don't do this.
It was a nightmare to potty train them and I followed the dapper rat instructions as best I could. The problem for me was moving them into the litter box on the off chance I found them pooing outside of the box. That was impossible when to get to the girls, I had to open up the crazy cage door and by the time I got it opened she'd have finished or bolted for her home because a giant hand was coming her way.
They had no specific corner they went in. They went in all but the food corner. That's when I read an article that said they generally won't poo in the same corner as their water, food or housing (not true btw- mine pood behind their house constantly). So, I put the water bottle in one corner, a grass ball home in another corner (got rid of the wooden colorful home I had due to its size and the wood soaking up the urine smell) and their food in another with the litter box in the remaining corner. Then I grabbed the biggest ferret litter box I could find and put some Kaytee brand smelly litter (mint or lavender- the rose smell made me ill) in it, crossed my fingers and prayed. I used YN for the bedding. They took to it almost immediately. I now have far more poop in the litter box than the rest of the cage. They don't poo in the grass ball corner, nor do they poo in the food corner. The water bottle corner tends to be a toss-up. But, the more poo in the litter box means less cleaning for me.
So ultimately what worked for me was simply putting Kaytee smelly litter bedding in the litter box and making sure the litter box was large enough for them. I think the combo of the smell and the different texture clued them in.
As for outside of the cage- when they are babies, every twenty minutes or so let her back in the cage to do her business. When she is grown, she will be able to hold it for an hour or so and you won't need to worry. It would be fine to just bring the litter box out with you when they are out so they can go. Mine like to play in it when it's outside their cage *sigh*. So I just make sure to either have the cage on the floor so they can run in when they need to go, or I just put them back after an hour.
I know training rats may sound a little funny but it is very helpful. You can train your rat to ride on your shoulder, to use a litter box, understand when you tell it no, and come to you when you call them by name. In order to train a rat you need to establish a trusting relationship. When your rat is comfortable with their cage and you then you're ready to begin training them.
The first thing you should start with is teaching them their name. When you see your rat say its name and then hold it. You must repeat this over and over but after a while if your rat starts to come to your hand when you call them give them a treat. Soon you will be able to replace the treat with petting or a kiss.
Once your rat has learned their name you can teach them to walk on a harness and leash. I use a ferret harness becuase it can be fitted to a rats size. Training a rat to wear a harness can be kind of tricky. Before a rat will walk on a leash they need to become comfortable with a harness. When you put the harness on your rat be prepared for them to squirm and wiggle out of it. Some may even drag their bodies on the ground to get the harness off. Don't worry, this is totally normal. Make sure the harness isn't too tight, you can check this by sticking your pinky finger under the straps. If your finger won't fit then the harness is too tight. Every time you put your rat in the harness give them a treat and let them know you're still there by petting them. Don't worry if your rat looks in pain or can't walk because they will do this to try to get you to take the harness off. Once they become comfortable with the harness they will be able to walk normally. After the harness training you can attach the leash. Let the rat wander around the house a little with you following. Every so often give a little tug on the leash and call your rats name. Over a period of time start trying to get your rat to follow you instead of you following them.
I think the hardest thing to train your rat is litter training. It is well worth the effort because in the end it will save you alot of money on bedding. I use the bottom of a kleenx box for the litter box but you can find a plastic one at pet stores. Put a little bedding in the bottom of the litter box and then place all the turds in the box. Every time you see a few terds outside of the box place them in the litter box. This may take a while but it'll work. Your rat will get used to smelling the turds in the box and will eventually relize thats were they should go to the bathroom. Good luck!