Establish good habits early
You know the saying: you can't teach an old dog new tricks. Get your pup used to a regular grooming routine early on so it becomes a fun part of its life. It'll make your life easier, with well-trained pups giving less resistance at bath time or when it's time for more awkward jobs, like brushing teeth.
Get the right tools
No matter what breed of dog you own, having the right tools is of the highest importance when it comes to good grooming practices. For starters, there are all kinds of different brushes - bristle brushes are good all-rounders, wire-pin brushes are better for dogs with thicker hair and rubber brushes are top-notch for short-haired dogs. Also, if you're clipping their fur at home, make sure you have good quality clippers.
Keep 'em smiling from ear to ear
It's especially important to clean your dog's ears if they swim a lot, as ear infections love a moist, warm environment. It's important to use a good-quality ear-cleaning product (don't try to DIY this part), follow the product's specific instructions and never use cotton buds or anything else that could potentially cause damage. Ear-cleaning can be messy so perhaps don't do this job in your finest clothes.
Everyone loves a mani-pedi
Most dogs, unless they're super-active outdoor breeds, will need their nails trimmed regularly. Depending on breed, this can be anywhere from once a week to once a month - you'll get a sense of the correct frequency pretty quickly (if you're unsure, check with your vet). If you're doing the trimming at home, make sure you have a high-quality trimmer for a nice, sharp cut. If you're not confident trimming your dog's nails yourself...
Know when to consult the professionals
When in doubt, take your dog to the vet or a professional groomer. You may not have to do this every time - many vets are more than happy to talk you through the proper way to trim nails, brush fur, brush teeth, and so on - but it can be a good way to make sure you're getting your technique right and using the right kinds of products for your pet.