Struts are pretty straight forward to replace - you'll need some equipment to compress the spring to get the struts out and a decent sized breaker bar to loosen the strut bolts.
As for the shaking, could be a number of things. Given the age and mileage - motor mounts would be my first guess. If it is due to the remaining, unchanged mounts, that is hard to say. Try jacking up one of the front corners of the car - don't need to lift a tire in the air, just enough to chassis a bit. See if the vibration changes. If you have a good floor jack, try lifting the engine slightly, enough to unload some of the mounts - you can lift from the oil pan, make sure you place some scrap wood between the jack head and the pan. You shouldn't put too much strain on the the pan - as you aren't trying to lift the car in the air - basically just barely holding the engine up. See if the vibration changes.
If the vibration changes in any of those cases, probably a good chance the other motor mounts need to be replaced. They are really tough to check visually, unless the mount is completely deteriorated. There is a chance that one of the replacement mounts is faulty - hopefully that is not the case here.
But since you mentioned that the shaking is less if the idle speed gets bumped up (AC kicked on when in gear) - there is a chance that your engines just needs a comprehesive tune up. Before you spend money on the mounts - trying getting a tune up. If you haven't had a tune up recently, now owuld be a good time to get one. Check plugs, plug wires, distributor cap and rotor. Check for vacuum leaks, fluid/filter change, clean/replace PCV valve, clean the throttle body. Also verify that the timing is within spec - if the timing is off or idle speed too low - you'll experience excessive engine vibration.