What are some strategies for using arty?

Shallow water makes it extremely easy for 'mechs to dodge artillery, so you should either try to secure the water terrain with your own units, or eliminate with a planetary condition. If you want to keep water on the board for your own 'mechs, earthquakes or beach might be a good PC to help your artillery by imobilizing enemies or giving them heat.

Alternate battery fire. If you have two artillery fire one and let the other rest so you can keep a constant bombardment.

If an arty unit is based by an enemy, it can't make arty shots, only direct fire shots. Providing an artillery with an infantry "meat shield" keeps basers away from them.

Also note that the non-artillery max range (NAMR) also denotes the minimum range for artillery attacks, so look for units that have smallish NAMR's.

Artillery units that have two pogs offer "more bang for the buck".

I've used artillery as an area denial tactic, especially in an urban environment where manuevering is tight to begin with. If an enemy mech needs to get into a particular spot to do an AO on me, I'll pog that spot, even if there's nothing there, and essentially dare my oppo to stand there.

Is it better to put a marker at the exact spot where you want it to hit, or move it a couple inches off, in anticipation of a missed shot?

that depends upon the accuracy of the unit. look at the marker and check the drift and blast radius. What do you need to roll to hit the unit that is over the marker be hitting spot on or drifting and staying at or within the blast radius. What are the odds of hitting that number? If you need an 11 or less without LOS, I will center dot a unit.