2000 Toyota Celica connect fogs light

What is going to break? The lights needs 12 volts and the battery is a 12 volt battery. What someone might have meant is you can't connect any wires to any battery by sticking them in between the battery's posts and cable clamps. That will seriously degrade those connections. You typically won't notice a problem right away but as moisture gets in there, the connections will deteriorate and cause problems later.

For your lights, the black ground wires can bolt to anything metal on the body or engine. Connect the two red wires together, but then we have to determine how much current they are going to draw. There's two ways to connect these lights. One is to run both red wires to a switch, and the other terminal on the switch goes to a tap in the fuse box. If each one of your lights draws 5 amps, for example, you need a switch that can handle 10 amps, plus a little extra for a safety margin, so you'd want a 12 or 15 amp switch. Something like that gets pretty expensive so that leads to the second method, and that's to use a relay, just like your horn and starter use. The switch can be very small and inexpensive. All it does is turn on the relay. The relay handles the high current for the lights.

Tell me how much current the lights draw and how you want to wire the circuit, then I'll draw a diagram and explain it.

Nope. Don't know which specific fuse, but if you use a test light you can find one. What I would like you to not do is poke a wire or terminal into a slot for a fuse, then shove the fuse in alongside it. That will get the job done, but it spreads the terminal in the fuse box. When you remove that added-on wire later, you will usually end up with an intermittent connection. Also, the strands of wire don't make full contact with the terminal like the blade of a fuse does. That less-than-perfect contact can introduce a little resistance. That translates into heat buildup and it's not uncommon to see melted fuse boxes from that heat.

Very often there will be unused terminals in the fuse boxes under the hood or inside the vehicle. You'll usually find one there that is hot with the ignition switch on. Keep in mind that you want any added-on items to be protected by a fuse. If you connect to a terminal inside the car, that will almost always be protected by a very large fuse under the hood that also protects a lot of other fused circuits. Those under the hood are typically 30, 40, or 50 amp fuses. It takes a lot to blow one of those. If your LED lights become grounded, (shorted to the body), their wires will likely melt before a large fuse blows. It's better to install an inline fuse holder with a more appropriately-sized fuse. Sixteen feet of LED strip lights draw around one to two amps. Two strips that long will draw less than four amps. A common ten amp fuse would be perfect for that circuit.