I find that shaving everyday causes huge irritation, as the hair hasn't had time to grow long enough by the second day so the razor hits the skin too closely. Leaving it too long can also cause irritation so I try to shave every two to three days and this keeps irritation down as well as leaving me smooth enough.
In between times, exfoliating helps prevent ingrowing hairs and likewise doing this before shaving helps lift any hairs and ensures they're picked up by the razor.
Sharp razor is essential! Start using a new blade as soon as the old one is the slightest bit dull, and moisturize regularly.
It's worth persevering with any irritation because it is worse when you first start shaving. Once you're into a routine where you're shaving regularly, this should cut down the irritation since your skin will be more used to it.
The alternative I've tried is waxing (at home) and it was not fun at all

The wax stayed on my skin and clung to the hair for dear life, it was awful! There's a funny story circulating about home waxing if you want to read it:
'WAX is not your friend' 
Some people swear by wax - I just swear at it. Pass me a razor over wax any day of the week!
Hope this helps, and hope the irritation eases for you soon!