We had Cookie easily trained with treats whenever she went potty outside. We also taught her the command 'go potty' so that we could be sure she did something. It still works very well like this.

With a small dog, it's important that you take them out straight after they finish eating or drinking. Puppies always have to go potty afterwards. And if they go, give a treat and say: good boy to go potty.
If they do it in the house and you see it, say a firm: NO. Don't if you haven't seen it. It's usuless and the dog won't understand and maybe even think he's wrong for being there.

At night we had Cookie in a giant cardboard box sleeping next to us (as a crate, but we found a real crate too expensive). We had her to go potty before going to bed and in the beginning we took her out around 3am. After a month or so, she could be in her box till the next morning.

Good luck.