Obviously this dog hasn't been trained!!
If he's peeing on everything, it sounds like he's also marking around the house. Again, something you need to train him not to do.
It's not just about taking the dog out multiple times a day. First of all, the dog shouldn't be allowed to roam around the house as he wishes until he's fully trained. Until then he should be in your your sight at all times or in a crate/play pen (with a pee pad) when you can't watch his every move.
Puppies generally need to go out at certain times like upon waking up in the morning, after eating a meal, after waking up from a nap, after playtimes and before bed. But you should always be watching him and taking him out as soon as you see the signs that he needs to pee or poop. And when he does do it in the right place, praise him and give him a treat. And don't shout or get angry when he does it in the wrong place (although you can say a firm NO), dogs (especially chihuahuas in my experience) respond a lot better to positive reinforcement.
Also something that helps a lot is feeding meals at specific times every day to make his potty schedule regular so you can expect when he needs to go out. If you're currently free feeding him (so he eats whenever he wants), I would recommend switching to 2 or 3 meals a day instead. Don't leave a bowl of food out at all time.
As for marking, you could try a belly band.