They tend to use different systems though- skills in one aren't necessarily transferable between each other.
Generally, however, the following works in turn-based tactics games:
A) Work out the paper/scissor/stone vulnerability orders. In Fire Emblem, swords beat axes, which beat lances, which best swords. In Advance Wars, Mech Infantry beat tanks, which beat recon, which beat infantry, and helicopters beat tanks which beat AA guns which beat helicopters.
B) if you have units that can inflict damage without getting hurt back, such as archers in most SRPGs, use them first. If the game engine allows return strikes, you are obviously better off using your melee units to finish off units which won't get to strike back and hurt them.
C) killing units to reduce the number of options the enemy has is better than crippling multiple units. It also has the advantage of simplifying the battlefield and making it easier to read for you.
D) in games with resources, like Advance Wars, a good mark of success is whether you are gaining more per turn than the enemy. Prioritise holding and defending resource points.
E) try to only engage in battles that are to your advantage. If you have to fight and can't beat an enemy unit, make sure it can only kill your lowest value unit while you prepare a strategy to beat it. This works particularly well on large enemy units that only get one move per turn- E.G. An enemy super-heavy tank can pretty much wipe out any one of your units per turn, so you may as well throw an already crippled unit to hold the bridge it wants to cross, buying you a turn to build an anti-tank gun for the lowest price. Alternatively, make sure the fight takes place where it limits the number of enemy that can fight and the amount of healing/repairs required from you. In Advance Wars, form your defensive lines on buildings to repair your troops. In most tactics games you can analyse the terrain to check which squares have defence/attack bonuses that might make them a good front line for you, typically high points and rough ground.
F) work out optimum formations and stick with them. E.G. APC units in advance wars resupply all units adjacent to them, so a formation of rocket launchers in a diamond shape can all be resupplied at once if the APC is in the middle. Same goes for any 'leader' abilities in SRPGs, e.g. An ability that mKes everyone stronger within 2 squares. Obviously you are better off moving that unit first and then have everyone else move and claim the benefit.
G) be flexible. Some enemy troops make being aggressive a better option, some make being defensive a better option. You are better off learning to play a game with a balanced selection of troops, as you will then have the knowledge of how to specialise from there, I.e. 'I need more archers/helicopters for this battle'. If you try to play with a broken list you found on the Internet, you just won't have the depth of knowledge to be able to adapt.