Susanne,
I got in the tub with my little one for the first few times. Then when I started to bathe him by himself, I sat him in the middle of tub and only filled the water up to the tops of his thighs. When cleaning the private areas, I'd just lean him over my arm and use the soapy washcloth. I also used(and still use) a big plastic glass to fill with water and pour on him. I always pour baby soap into the running bath water while its filling to get it nice,bubbly,and soapy. The hair washing is the hardest part,but if your little guy doesn't have much, you can use the washcloth. Mine had a bunch of hair from birth and now at 18 months its a big mass of unruly curls. I cannot for the life of me get him to lean his head back, so I have to cover his eyes with a wash cloth and use the glass to pour water over his head.
I never used a bathseat. Just a plastic mat(Target) on the floor of the tub so they don't slip and slide. :)