Gently, carefully, and rarely.
My two sows have only received full baths twice: when they came home from the shelter and after I switched them to fleece from aspen bedding. Aside from that one usually gets a butt bath every couple months since she's kinda messy :/
Maggie is a big baby and whines whenever something doesn't go her way (like getting her foot rinsed after she smooshed it in poo). I generally calm her down by petting her on my lap for a few minutes and feed her a treat. She gets a firmer grip during her bath since she's jumpy too. Speaking/singing in a soft voice helps too; just think of them as furry infants
Afterwards she gets a treat.
I take them one at a time to the sink, which I make sure is pre-filled with an inch of tepid water (running water scares them). I gently place her into the sink and wet down her fur by scooping up the water with my hand. Then I use about a pea size of Bunny Bath (which is recommended by lots of other people on the forum since it's very gentle), rub it in my hands to foam it up and then gently rub her coat with it. Avoid the face! After that I rinse her off a couple times with the same water, then empty and refill the sink with clean water for a second and third rinse. If the chin is dirty, I'll usually wipe it clean with a washcloth.
From there, they usually hang out with me on the couch in some fluffy towels until they're dry.
My pigs are short hair so I can't really help you with the trimming part. Sorry!