Grooming is a huge part of basic animal husbandry that when you purchase a dog you are also taking on the responsibility of keeping them healthy through regular grooming. This includes bathing to keep the skin clean, brushing to prevent tangles or impacted undercoat, ear cleaning and of course - nail trimming.
Trimming your dogs nails has many benefits from preventing them from breaking off if they are too long, keeping floors or furniture or skin from getting scratched up, and preventing health issues from developing in your dogs feet. Nails that are too long will push the toes uncomfortably up or pull them away from each other. The nail can also start to curl and eventually grow under the foot and puncture the paw pad. This can be painful for the dog, cause infections in the foot or even cause lifelong pain from the toes not sitting properly when walking.
But nails also play important roles in your dogs daily lives so they should have some length to them. Dogs may use their nails for grip, stability and traction when turning while running.
Ideally the nails should not touch the floor when your dog is standing comfortably on all four feet. However some dogs have flatter feet than others which makes the nails touch even at a shorter correct length so if you are unsure how long your dogs nails should be, talk to a professional groomer or veterinarian. In some cases you can go by the sound of the clicking on hard surfaces however this is not always the best way to determine if your dog needs their nails done. Some dogs click all the time even with short nails because of how they walk or the shape of their feet. Some dogs may never click when they walk even with nails that need to be trimmed. Nails that have been trimmed too short can also affect your dog and it is usually unadvised to create "nub" nails where there is hardly any nail left on the foot.
Part of a responsible owners job is to provide training and conditioning for their dog to get them comfortable with having routine care procedures done including nail trims. Even if you plan to take your dog to a groomer or veterinarian to have their nails trimmed, you still need to make sure you are working toward making sure your dog knows how to behave.
Handling your dogs feet is a great way to start but its important to combine it with something positive such as a high value treat (hot dogs or peanut butter). If a dog does not enjoy having their feet touched they will never magically just accept it if you play with them constantly without providing a positive association to it. All it may do is make the dog dislike it more. If I hate being poked and someone continues to poke me in an effort to "get me used to it" I'm never going to decide I'm ok with it. I may however start getting grumpy when someone goes to poke me. However if every time they poked me they handed me $100, eventually I'd be okay with dealing with being poked even though I still didn't enjoy it for the sake of getting the $100. So while handling your dogs foot let them lick some peanut butter or eat hot dog bites. They will start looking forward to those handling sessions.
Willa working on her nail trim manners