The easiest way is the black hat way using proxy/ips. I am not sure if it can be necessarily labeled black hat but anyways...
The clean way is to have a direct link to google with the search terms - put it on high traffic pages and ask visitors to click it and find your website.
Firstly you are increasing the search count and also the likelyhood of it getting included in the Auto Suggest list of google.
2nd, you are getting your visitors back.
You can make it interesting like a treasure hunt, give them a discount or a freebie.. to go to Google and be able to find their back.