Yes, you can give loratadine to dogs, it is usually well tolerated and is unlikely to produce side effects such as drowsiness that tend to happen with some of the older antihistamines, such as diphenhydramine (also known as Benadryl). The human form of loratadine is the same as the form administered to dogs and it can be purchased at any drug store or grocery store.
The usual dose of loratadine for dogs to relieve allergies is 0.12 mg/lb to 0.22 mg/lb (0.25 to 0.5 mg/kg). For example, a 20lb (9kg) dachshund would require 4mg of loratadine but a German Shepherd weighing 60lbs (27kg) would require approximately 12mg of loratadine. You should always talk to your veterinarian first about the dosage before you administer it to your dog.
Loratadine is available in 5mg tablets, 10mg tablets, and syrup. Tablets are best to give to dogs, so round up or down the dosage to the nearest half tablet. For example, if the dosage works out to be 4mg, give one 5mg tablet. If the dosage is 12mg give two and a half 5mg tablets (makes 12.5mg).
And when buying loratadine, make sure the product you buy only contains loratadine, because some products combine loratadine with a decongestant (such as Claritin-D) which can cause side effects in dogs such as a rapid heart rate and pulse and anxiety in a dog and possibly worsen the allergic condition you are trying to treat.
Claritin syrup is preserved in propylene glycol and should not be used in cats. Oral disintegrating loratadine tablets (also called "orodispersible" tablets) may contain xylitol, a sweetener which is toxic to dogs and should not be used in dogs.