When running through a firewall your most important issue is to avoid knicing or cutting the insulation - that means good cut resistant leadwire and a grommet around the access hole oyu are using. Normally there are a host of firewall holes with rubber or plastic inserts (grommets or sorts) that you can fish the leadwire through. I will assume you are using one of those for this discussion.
First you need to know what kind of current (power) is being drawn - WORST CASE - on that power lead. Calculate the max current that will be passed through the wire. the math is easy. Locate the POWER (in watts) of the load (ie the amp or whatever is being supplied) from its nameplate and divide that number by 12 (12 volt system is assumed. So if it says 100 watts - 100/12 = 8.3 Amps through the wire. In most automotive applications the wire of choice is SAE lead wire like GXL or SXL or TXL. You can also use THHN building wire but it is very stiff but resists cutting. The SAW GXl styles are readily available at most auto stores.
You can look up readily the wires rated current carrying capacity in most any reference book. DC (in cars) is full duty cycle unlike AC which is not so wire is derated slightly. So use overkill. Normally you can run 12 AWG for a load of 10-12 Amps coninous (144 wats) - with safety. Larger for more power. Your auto store who has the wire will be able to look up the wires "ampacity" Select a lead wire that is a different color from the others in the vehicle - this makes it easier to spot when running or troubleshooting. Purple works well LOL Do not use green or black which are colors for grounds.
Route the wire away from other wires - dont bundle it too tightly - the more confined it is the hotter it will get and the amp rating is based on heat buildup.
Once wired to load (amp or lighting or whatever) - you need to hook it to the main power source. This may be the vehicle battery normally. IT MUST BE FUSED - to do otherwise is putting your vehicle at risk for a fire. Though it is possible to wire to the main fuse housing where all those little AT and ATO fuses are - and using a spare position - it is suggested that you simply use a separate pigtail type fuse holder -one that has the leads eminating from the black housing - the fuse inside is usually a glass 3AG type but there are holders that use the small axial tang ATOs like most cars use now. I recoinmmend sticking with ATOs because they are so readyy available.
Wire the fuse holder between the power source (battery) and the lead you installed to the load (amp etc). Make sure the splice is neat - not exposing any bare wires and is mechanically sound so it doesnt fall apart. tape it or cover it with heat shrink tubing if possible, Splce it into the battery lead with the fusable link on it if possible. You may also elect to locate (car schematic) a power lead that turns off when the car is off - so the power is automatically disconected. Otherwise youmay leave the amp (IE) on by accident and draing the battery while it sits idle.
The fuse you select must fit the load (amperage) you are drawing with some reserve. If you calculated the max currect at (IE) 10 amps. then use a fuse that is 50% higher than that value so use a 15 Amp ATO. if its 20 amps use a 30 Amp fuse. Make sure the fuse is secure - sealed - cant touch anything and I suggest you cable tie or tape the fuse portion to the main harness or some INSULATED surface - but stay away from hot things - heat will derate the fuse and cause it to blow ruinng your best album track.
You will need to possible run a separate ground lead which would be the same gauge (AWG) as the power wire you just ran. that must be connected normally to the load (amp) and routed either back to the battery or at least to a solid chassis ground. Make sure this is a good connection also or you will have intermittent problems as it makes and breaks. Locate it where it won't get tangled or hitby something that might rip it out. Once both leads are in place and the power is connected - power up the system by turning on and off the ignition if its supposed to activate the load. Use a voltmeter DMM or other 12 Volt sensing meter (some cars are higher voltage now so check first).
check that 12volts goes on and off with the power wiriong scheme you have. I dont recommend every having it connected hard wire to the battery for the drain reason. anchor all power wires well with cable ties or tape along a path in the trunk or wherever it is wired - (ie under dash) so they are not hanging - cant get caught in something and are securely anchored. you should be all set then
remember - figure amperage then wire size - then fuse = 1.5x figured amperage - then nearly wire and then nearly tie down all wiring and test and look it over twice - three times even. Electrical fires are a cars worst enemy