i would like to install a power inverter so i may run the aircon
I reckon that you'd struggle, aircon uses a great deal of power. Look for a rating on the unit.
what size inverter will i need to run a small tv, dvd player, lamp, maybe the car stereo as well.. what sort of second battery will ineed to power this and will i need a new altenator or can i hook up a solar powered charger for the second battery.
You may find you need a pure sine wave inverter to run a DVD and TV. The key is in the wattage of each appliance - to run an 80W light bulb you need a 100W inverter etc. A car stereo would run direct from the 12V and not need an inverter. To run that lot for any amount of time you'll need a large solar panel (maybe 80W - £300) and at least a 120AH lesiure battery. I have 160W of solar, 360AH of battery and a 600w PSW inverter and it's great when it's sunny but pretty shite in the winter to be honest (I power a desktop PC with it (this on as it happens!) and it doesn't keep up with the usage).
Charging from the engine won't need a new alternator as the draw for battery charging is small compared to (say) a fog light.
Edited to add - from your other post I see you're in Oz - in which case you're OK for sunlight!! So you could start with a smaller panel (say 20W) and if it doesn't keep up you can add some more.
If you get 5 hours good sunlight on a 20W panel you can power 100W of equipment for 1 hour etc