This dish is almost too simple to be an actual recipe, more of a suggestion. So if you need another excuse to make aioli (or force yourself to learn) here is the link to my post with all the tips to ensure success.
As for cooking salmon perfectly, make sure your pan is really hot and that you have a cover for the pan (preferably one that does not fit snugly). Unless you are blackening the salmon, only cook it on one side, skin side down, and cover it to steam it so that it doesn't dry out. Remember that salmon is similar to any meat you cook and will continue to cook once removed from the heat source. Once the white stuff begins to ooze out of the flesh (which you can scrape off for a more appealing presentation), it is getting close to being done. Don't be afraid to stick a knife in the center to see if it is cooked through. The flesh will turn a slightly duller color when it is cooked and you can also feel how the flesh is firmer once cooked. You do want the color to change all the way through the fillet but just barely so that it is not dry.
Pan Fried Salmon with Aioli
2/3 lb salmon filet
aioli (make your own)
Make aioli and chill in the refrigerator. Heat a skillet over medium high heat for 4-5 minutes. When hot, add oil to coat the bottom and add salmon skin side down. Cover and cook for 10-15 minutes until salmon is cooked through - white foam will begin to appear on the flesh and you can scrape it off. Salmon should be cooked through, it will change to a slightly lighter color and the texture will be firmer. If you like, toss in the capers and crisp in the cooking oil.
Remove fish from pan by carefully lifting if off its skin and cut in half. Spoon aioli over top and garnish with the capers.