Google is your friend here. You're asking about the broad, broad basics of 'writing' as bare as 'what pen do I use'.
Write down everything your instinct tells you is worthy of putting on paper. Everyone's starting out material is stuff they later look back on and think 'what was I thinking', so get all your stuff down and it gets better and better.
Stand up specific; based on my own newbie experiences...
All depends on your personality, what kind of person you are, that ultimately becomes your voice. Some people are into 1-liners and puns, and whilst it's distanced from full on soul-baring, it's still a craft that requires wit, a turn of phrase and hard work.
Stand up (the kind that matters) is about telling a truth that is otherwise left unsaid in public. Then, once you find whatever it is that offends your sense of reason, you have to word your ideas so that they become 'jokes' and 'bits'.
Then there's the "wacky" stuff, where the laugh isn't from the wording/ideas in your comedy, but the actual delivery/presence, where people laugh at the fact you're eccentrically shouting/using physicality, as oppose to laughing at what it is you're actually shouting. "funny"
The more popular route is the whimsical observational stuff, that doesn't really have any rage or bloodlust behind it, where you notice stuff, comment on it, soak up the applause and move on without having made a point...
There's really too much to say on the subject - Log onto stand up forums - Chortle, Manchester Forums, Yorkshire Forums and Midlands Forums and each site contains a message board "Gold" thread, where the topics spanning the last few years are retained. Here you'll find hours and hours and hours of tips, anecdotes and insight to get your cogs turning.
On this site there's a few really funny people who do stand up, Bussell and Miss Wicks, Chopz, Cowards is a pro, plus loads more. There's Alski, Jason S, Scaffardi and a few others starting out so do a BCG search for "Stand Up" and you'll see loads and loads of years worth of threads/vids/feedback/tips and shared insight/ideas in threads that collectively form a priceless education.
The simplest way to start, is to realise what TRULY makes you laugh and touches a nerve/funnybone? You won't be able to perform the kind of comedy that you hate, so, you'll probably try in the vein of comedy you love. Take it from there and your voice'll find itself, the details'll take care of themselves.
As for asking "what to write in a notebook" etc, that's silly. Everyone does their own thing. The more typical thing is to write wherever, on whatever possible, then, when at your computer or writing pad, you take all the napkins, Rizzla packets and various bits of torn paper you've scribbled on throughout the day and shoehorn it all into something coherent.
PS - As soon as you get something down on paper, rewrite and rewrite and get rid of any surplus then try out open mics. Getting comfortable behind a mic is a separate issue from writing and a whole other problem, one minute you're in a packed comedy club on comp night, the next (more often) you're talking to about 10 people in a pub who want to watch football.
Also, check out the numerous blogs from stand ups and they paint a picture of what the venues/crowds/bookers are like and how it's all a million miles away from McIntyres Roadshow.
Finally, and most obvious, soak up every single album/special you can from the 40's to present day. Good comedy, bad comedy, all in between. Educate yourself and obsess over the history of stand up as it evolved and become aware of everyone - a simple Wikipedia search of british comics brings up about 1000 results, US comics another 2000. Check out podcasts by Mark Marron, Joe Rogan (especially!!) Adam Carolla, Doug Benson, Duncan Trussell each contain literally hundred of hours of interviews with stand up comics discussing the mechanic of stand up comedy styles, week in, week out.
Spend a sleepless month or so obsessing and reading and writing and your passion should carry you through. Then, you'll emerge a lot more prepared/empowered than you are now.
Good luck fella, it can be fun.
