The reason that I put fishing and cooking together is because once you are a fisher you would usually want to cook and not waste your food. It is a much easier way of making money than having just one of the skills. If you are a cooker then you don't have much to cook and if you are a fisher than you have raw fish for no reason.
First start by buying a fishing rod from the grand exchange and buy some bait, about 200. Or the other option is to buy a fishing rod and bait from Port Sarim. Now you have a fishing rod, bait and a small fishing net.
Now since you have all the equipment needed you should go to Al-Kahrid and start you're fishing career. Al-Kahrid is the ideal place for beginning fishers as the bank is extremely close to the fishing area making it very convenient. Use your net to start and catch shrimps until you are level 5 when you can switch to your fishing rod and catch sardines. Once you have got up to level 10 and are able to catch herring get all of your sardines and shrimps and go to the range in the kebab shop. Here you will cook more and burn less ass it is not a bad fire. Cook all of your Sardines and shrimps now your cooking level and fishing level will both be around level 10. Now store all of your newly cooked food in your bank. Now keep on fishing. You will get a 25% chance of getting herring since you have just started being able to fish it. Once you got to level 15 you were able to catch anchovies with your small fishing net. Catch these for a while until you are level 20. Once you are level 20 you should cook all of your sardines, herring and anchovies on the range.
Now you have gotten to the next stage of fishing. To get your equipment for the next 40 levels you will need a fly fishing rod, a harpoon and a lobster pot also you will need feathers but I advise you to kill chickens if you want to save money. I advise you to get all your equipment from Port Sarim as you will not need to wait if you buy it from here. Now you should go back to Lumbridge go on the side of the river in which Al-Kahrid is on but don't actually enter Al-Kahrid. You will now need to use your fly fishing rod and feathers. Now fish for lots of trout until you are level 25 and get your fishing rod and bait out. Store all of your fish inside the Lumbridge castle bank. Now fish some pike. Once you have finished fishing your trout and pike and you are level 30. Then you should go and cook it all in the Lumbridge castle range. Now you should get your fly fishing rod and feathers again. Fish for salmon and trout until level 40 by now you should have plenty of trout and Salmon, cook all of it. Although you are able to harpoon tuna by now you should not until you are level 37 fishing as these extra 2 levels give you a great advantage when getting tuna. It will get you much more tuna at a time.
You have now entered the stage of advanced fishing. To start your first go at harpooning you need to go to Karajama to fish for these. Go to through the banana plantation and get to the dock where there are multiple fishing spots for everything. Once you get to level 40 fishing and if you are cooking all your fish than your cooking level should be way above level 40. Now is the time for cooking and fishing lobbies. One of the best market items for selling. It is an extremely popular food and you will almost always have immediate sells at the grand exchange. You will have to fish and cook lobsters for 20 levels until you are level 60 and are able to fish the best non-member food, swordfish. These heal 14hp at a time! You may think that this is long and tiring and grueling but in the end its worth it!