Serious problems during DNA extraction from swabs is that most of the samples are attached firmly to the swab. Therefore, I recommend you before collecting samples first pre-wet the swab with sterile PBS or water, which give you maximum samples and good results.
For DNA extraction you can use MO-Bio or Qiagen kits, both provides good quality DNA.
There is no any precaution but you must work asptically in last step ( DNA elusion ) to avoid any contaim that may be affect on extracted DNA like bacterial enzymes.