Welcome, I have an Oklahoma Joe offset, when I first started I had that problem because I wasn't getting a good bed of coals going before I put my meat on..my wood was still putting out creo which is very bitter, and putting out too much smoke.
What I do now is put about half a chimney of coals on leave all vents wide open even leave the fire box and cook chamber doors open. After they ash over I put on a split, close the FB door only for about 15 mins then close the CC door and start to bring things up to temp. This process takes at least an hour and half before I can put on any food in the CC, this will give you time to get the smoker up to temp and burning right, leave all your vents open full until you get the temps up to anywhere from 200 to 225, you'll have to get a feel for when you need to start shutting down the vents to stabilize your temps, every smokers different, even the type of wood you use changes things a bit. But like was mentioned, keep your next split on top of the fire box it will start faster and smoke less when you put it on, don't put any wet wood in there only dry. Your looking for thin smoke, doesn't take a whole lot wood when you have a good bed of hot coals. Don't put any food on until you have stable temp and good thin smoke. On my smoker by the time I put on the food, my FB vent is barely open maybe a quarter of inch, I can maintain temps with a single small slit for more then a hour and a half, for a 5 or 6 hour smoke I may only use 3 or 4 splits. But keep in mind to do that you need to have a very well sealed smoker to do this, air causes more fire more heat more smoke, so fire management is a very BIG part of offset smoking. Best advise I can give for anyone with a new smoker is do a dry run just like you were doing a smoke to get a feel for how your smoker is going to react.
The last thing you want is be experimenting with fire management with some expensive meats in your smoker paying for your leaning curve...lol...what most new pit masters do is end up chasing the temps, temps get low they panic put too much wood in or coals, the temps shoot up to 400 degree, they panic more start pulling stuff out or shutting off all there vent open the CC doors, and the temps nose dive to 150 degree well you get the picture, I did it, I venture to say every one here has done it..lol..practice runs will help prevent a good deal of that from happening. Good luck lots of folks here to help