People react very differently to nicotine... you got what cigar lovers have coined "nicotine sickness."
Firstly, drink LOTS of water WHILE you smoke... between EVERY puff. In fact... you SHOULD drink a lot of water thoroughout the day, as well... a well hydrated body absorbs (and gets rid of) nicotine much easier.
Secondly, always smoke on a FULL stomach...
Thirdly, smoke outdoors and sit somewhere where there is good air-flow (use a fan if you must)... so you don't inhale much smoke.
Fourthly, get GOOD sleep EVERY day... not just after you smoke.
Fifthly, smoke QUALITY cigars. Some cheap stuff out there has a whole mess of chemicals, hasn't been well aged, isn't well balanced from beginning to end, etc... Smoking premium stuff can help to ensure you're not ALSO ingesting a lot of crap that helps you feel sick and ensure that your nicotine intake will at least be more regular, if that makes sense.
Lastly, stand up every so often while you're smoking! This will help your circulation and can ease the affects of nicotine sickness (or if nothing else, help you to recognise the symptoms early on so you can take a break and drink some more water).
These are the BEST things you can do when you're one of those people that has a very low tolerance for nicotine... or just got nailed once by a particular smoke. I've helped a couple buddies through this and... over time... they developed a higher tolerance. You can too... but you NEED to start out by doing these things and letting your body ease into it!
Hope that helps...