Find a yellow Power Armor Station and walk your suit up to it and get out. Don't get out of the suit next to the Power Armor Station, it needs to actually be hanging on it. Mouse over the station like you do with any of the workbenches and choose Craft (E).
You can then mouse over the part of the suit from the inventroy menu at the bottom left and click 'T' to repair it.
It's from here you can also add mods to the parts, just like you do with your weapons and armor.
You can not recharge Fusion Cores. You can find them around or buy them from certain traders such as Cricket in Bunker Hill.