If you see dripping and you need pots to collect the water, then it is a definite sign that you need to call a roofer. And if you see dripping, you probably have some other damage as well. As soon as the weather gets better, you should get a contractor to come out to assess the damage.
If your roof is buckling, it is a sign that it was not installed properly or it does not have enough ventilation. You could try to do it on your own, but safety is an issue. You will need to replace some of the shingles or maybe even install additional ventilation. This is one of those things that are better left to the professionals as they have the requisite safety training.
If you have dry rot around your roof, then it might signal an even bigger problem in areas that you cannot see. Dry rot pretty much renders the wood useless and unable to support weight. These need to be repaired before they get worse. You can either take out the dry rot or put filler in it to replace the wood altogether. Of course, ideally, you would want the wood replaced and treated. Then of course, you would need to fix the leaky roof.
If you have a skylight and water is coming through, you might need to call in the professionals. You might be able to fix minor leaks with sealant, but if it’s a major leak, repairing it will require more know-how and experience.