The small inverters (400 watts and under) come with a cigarette lighter adapter, and may be plugged into your car's lighter socket (although you will not be able to draw more than 150 to 180 watts from the cigarette lighter socket). The small units also come with cables that can be clamped directly to a battery. If you want an inverter that will plug into your cigarette lighter, you must choose one that is 400 watts or less.
Larger inverters (500 watts and over) must be hard-wired directly to a battery. The cable size depends on the distance between battery and inverter, and will be specified in the Owner's Manual.
When connecting the inverter to the battery use the thickest wire available, in the shortest length practical.
Inverters 1500 watts and under: If battery and inverter are within 4', use #4 gauge AWG. If 4'-6', use #2. If more than 6', use #0 gauge wire (#0 gauge wire may require a "0 to 4 Gauge Adapter"). The maximum length generally recommended is 10', and shorter is better. If you need more length, it is much better to put it on the AC side (as with an extension cord from inverter to appliance) than on the DC side.
Inverters over 1500 watts will require #1/0 or larger cable, in the shortest possible length.
A few specific recommendations:
Xpower1200 - #2 cable 3 long
Xpower1750 - #1/0 cable
Xpower3000 - #4/0 cable