In order to get the longest life from your teak furniture especially the outdoor ones, it is important that you treat the teak wood at least once per year to maintain its water and insect-resistance and to prevent splitting or warping.
What you need to prepare are teak oil, dusting rag, oiling rag, and well ventilated area. Then you can start as the following instructions.
First, with a dry damp cloth, dust the piece of furniture so that you get every bit of dust off of it. Use a bit of elbow grease if something actually dirty. If it is really dirty you can use oil soap. Allow it to dry completely.
Second, open the windows. Teak oil is very toxic so you should either take your furniture outside or apply the oil where you can open some windows so you don't gas yourself out.
Third, apply teak oil. Using a clean cloth used to Teak Oil, either to put the oil on the cloth, just pour some directly on the surface and start wiping it in. You don't want pools of oil to stay sitting on any surface, so wipe it in and sop up any excess. It will stay shiny and sticky to the touch, so don't put anything back on top, allow the oil to be absorbed.
Fourth, reapply oil. After an hour, check whether all the oil has been absorbed by the wood. If you still can see dry spots, reapply the oil and allow it to dry. Make sure to wipe the top of the teak oil can before you put the lid back on otherwise you will have a heck of a time trying to open it the next time you need to oil.
Fifth, let it dry perfectly. Allow the final oiling to dry over a 24 hour period so that it will be absorbed perfectly. If you're finding that you used too much, wipe up the excess with a clean cloth. Please not that teak can absorb quite a lot of oil.
Sixth, maintain. Now that your teak is shiny and new looking, make sure to use coasters under glasses, dust it frequently and try not to have it in direct sunlight as this will expedite fading and drying out.
With a little bit of care and maintenance you should get many years of enjoyable use out of your outdoor teak furniture.