in order to die from cutting(veins method) you need to be sure that:
blood won't clot(alcohol, blood thinners, hots bath, aspirin wouldn't work i used it and failed miserably)
you won't chicken out and cry for help, death from bleeding is long and nasty, if you go down the road route i.e cut veins vertically and wait for the result there's enough time to reconsider your choice though after you slowly loss too much blood you will feel so bad and tired so only options left is to await the death
you will use good sleep drugs if you want to injure yourself and bleed to death asleep, there's a decent adrenaline dose in the process of self-mutilation so one to several pills couldn't work
you have enogh time, in case of bleeding without any or with weak blood thinners blood as time passes will leak slower and slower, it's organism adaptation for bleeding, so it can take even 5 hours, i was close to death after 3 hours passed
next factors to consider is thickness of your skin, too much fat make it harder. second is the place you cutting , arms have more tightly packed venous network so you will bleed faster if cut arms, but you can damage tendomds and nerves which is potentially can lead to disability, so to me legs are better though it would take longer
for arteries it's much easier i once stabbed myself with a 1.5cm long pointed head of heat wood carver in femoral artery, i was underweight tho so it was not much to pierce in, blood spurted out for 30 seconds and it's then clotted unfourtunately, i didn't used any means to prevent blood clotting but spurting was fascinable and my last thoughts was 'lol'. caveat is that nervers are close to arteries if you look at anatomical atlas. cutting in a wrong place and you disabled from a severed nerve. look at femoral, brachial and radial arteries if you still interested. cutting neck is tough and as odds to die with this method are ridicuously low so don't consider this method please unless prepared to wear ugly visible scars lifelong(no job and people look at you like on lunatic). for tools you should decide yourself, but people recommend scalpels but it's possible to inflict serious damage with a common razor blade
with CO there' less hassle. in your case when there's no car and avaiable room my choice would be hide in a bag some charcoals and roam in an basement of some abondoned building, find some room of small volume then cook coals until prepared in a corridor, bring smoldering coals in a room and lock myself and isolate it ventillation. CO meter is required , when ppm on the meter reaches 1000 you'll know that you're done