You didn't say which version of Fish Tycoon you're playing. The different versions use different trial modes, but all of them are restricted in some way - either a time limit or feature limitations.

When the game says "Please register" it means that you need to buy the game. Upon purchase, you will receive a registration code that will unlock the full game.

Keep in mind that registration codes for the Windows version are different for each site that sells the game. If you download a demo version from one site, but purchase the game from a different site, you'll need to download the game again from the site where you made the purchase in order to use your registration code.