Board Thread:Questions and Answers/@comment-25441082-20170705013509/@comment-29421682-20180301160630

When Spider-Man rescues John Jameson from the Chameleon on the space shuttle, it's revealed that there were multiple alien embryos and spores on board. The surviving embryos and spores are then shipped to Horizon Labs.

Then, after Spider-Man's first fight with the Lizard, there is some of the former's blood left over in Curt Connors' lab. This, combined with the alien material, results in the creation of the symbiote.