Getting up on your roof can be unsafe – both to the roof and to you. You can damage the shingles or tiles by walking on them, the roof may be slick or at an unsafe pitch, or your roof may be soft in some places and cause you to fall through. Here are some safe ways to inspect your roof for damage:
– Hire a roofing contractor who offers free estimates. This is probably the safest way to go, as a knowledgeable roofer will be able to let you know if you have a current issue, if there is something you should do to 
prevent future issues, etc.
– Prop a ladder up on a dry, flat surface and take a look yourself. Remember to wear rubber soled shoes if you’re planning on mounting a ladder! Also, try to wait for a dry period so you can see your roof properly. Unless you are looking to see where water is pooling, looking at your roof while it’s still wet can disguise damage as the water can darken your roof and hide issues.
– Do a visual, “from the ground” inspection. You can grab your binoculars or even your camera phone to take a look at various angles of your roof and inspect for damage from the ground. Another idea is to go under the eaves and look for any damage there.
– Do a touch test. Go into your attic and feel the ceiling for damp spots. Good places to check are around vents in your roof, around skylights, around your chimney, and in any spots you suspect a leak. If your attic is wet on the inside, it’s definitely time to get your roof fixed before the leak gets worse.
Overall, just stay safe and do the best job you can when doing a DIY inspection. If you are getting a roofer to do the inspection, make sure you understand what to expect from them, and that you choose a roofer with good reviews or who has been recommended by others.