I have a 800 w solar array with 350 ah lithium battery storage and a 3000 w inverter how or can this be hooked to my on grid system or will it back feed and short the inverter thanks
That system should provide a good backup in the event of grid failure. If you are very careful you may be able to run a refrigerator plus a microwave oven for brief periods of time.
You will need to contact a professional installer so that your grid connection is installed in accordance with local, state, and federal code. It’s not something you want to fool around with as a mistake could cause a fire or hurt someone. Also, your insurance is unlikely to cover the cost if it was not certified and installed by a professional.
As a parting thought, you may want to consider the installation of an AB switch such as the one pictured below. This would allow you to manually connect the inverter into your main breaker box and power select loads. For example, in my previous home I was able to power a few lights, the refrigerator, microwave, well pump, and the furnace. Not necessarily at the same time as my generator had limited capacity.
In most jurisdictions in the USA you will need to use a licensed electrician and have explicit permission from the electric utility to feed power back into the grid and get paid, or recieve credit, for it.