There is no official sandbox mode in RCT2 as far as I know, but most experienced RCT2 players have created their own version of one at one point or another, so you will see something like it in YouTube videos as well as downloads here at RCTgo.
1. Go to Scenario Editor. This can be accessed through the red toolbox on the far right of the main menu. You can use this to build any park from scratch, but these instructions are specifically for how to build a sandbox mode for building rides and saving them with scenery in an open park environment.
2. Check the boxes for every roller coaster and every ride that can be customized in any way, such as Go Karts, Observation Towers, River Rapids, etc. If you have Wacky Worlds or Time Twister installed, just check the rides available for standard RCT2 to avoid going over the limit.
3. Make as much scenery as you can available. Since there is a maximum number of scenery themes allowed in a scenario, there's a simple way to do it and there's also a way that takes a bit more time. You could just check the scenery types you use the most--essentials for me being Mine, Medieval and Mechanical, to name a few--and leave it with those options. If you want even more options for your sandbox mode, you can click the Advanced button, which gives you the option to select individual scenery items rather than entire themes. So if you want particular walls and blocks but don't want useless smaller items, you can check and un-check as you please.
4. Make your map size as large as possible, then select "Land Owned" and fill the entire park so that only the edges of the map, which can't be owned, are outside of your park. Don't forget to put in a park entrance and a path leading there from outside.
5. When you're on the Invention Setup step, make sure that every item is available from the beginning so that you don't have to wait for any research any time you decide to use your "sandbox" park. Nothing should be under the "Items to invent during the game" list.
6. When you get to the point where you see a box with monetary values, check the box that says "No Money" and your scenario will be free of financial restrictions. You shouldn't have to check any other boxes after that on that step.
The Scenario Editor is remarkably easy to use, so most of this will come pretty intuitively.
If you become a proficient enough RCT2 builder, you may just be lucky enough for one of your downloads to be featured on your birthday.