After surveying the place you have the option to make an offer or to coerce them…
How to Make an Offer
As Corinthas points out, the option is in the journal under the decisions tab. You need to do the survey, then click the event on the right side of the screen after the survey completes, choose the buy or force options.
If you choose the purchase option, you need at least positive 20 relations with the country Egypt or Colombia depending on which canal you are building.
Once you hit that relations threshold, go back to the journal and the check mark button should be lit up. The cost is cheap, much cheaper than a war would be.
Once you purchase the land, select your new tiny province and go into the buildings tab and build the canal. Wait for 90% employment and the even will finish with success.