The terrain editor works exactly like in UnrealEd 3.0 from UT2003/2004.
The only exception is that the heightmap cannot be created "on the fly" in the editor. You have to make one outside.
What this means is that you have to created a greyscale texture, import it, set it as your heightmap in your TerrainInfo and then, in the TerrainEditingTool, convert it to 16-bits.
I had a tutorial on my website for this, but it's currently down, so I'll run you though the basic steps. I assume you are used to creating terrains with UT2003/4.

Create your empty cube, add the usual zoneinfo with bTerrainZone = true.
Add your TerrainInfo.
At this point, everything you can do to your TerrainInfo will crash the editor. This includes moving it. One the TerrainInfo appears in your 3d viewport, do not use the viewports anymore until I say you can.
Open the Texture Browser and import an heightmap. This should be a greyscale texture with usual and additional limitations: size has to be a power of 2, the texture has to be square.
Once the texture is imported, open your TerrainInfo's properties by clicking the Open Actor Properties button (do not double-click the actor in the viewports).
Under TerrainInfo, in the TerrainMap field, add your newly imported texture. Rebuild the map, you can now use your viewports.
The TerrainEditingTool will then work just like in UT2003 and 2004, with two important exceptions:
1) It might crash randomly for no apparent reason. Save often.
2) You will not be able to alter the terrain's geometry (ie: the heightmap) with the sculpting tools such as Flatten, Painting, Smooth, etc. In order to have these tools work, you have to open the TerrainEditingTool, right-click on the Heightmap and select "Convert to 16-bit". This is supposed to turn your heightmap into a G16 texture which is 16-bit greyscale. However, this does not seem to always work. I suspect it can only change textures which are in specific formats. BMP seems not to work, so if the conversion fails to make any change, try with an imported .pcx heightmap.

Alternatively, and this would be my recommandation, you can skip this whole thing by creating an heightmap of the desired size in UT2003/4 through the usual process, leave it blank, export it to your desktop and import it into Unreal2. It will work fine and provided you don't crash the editor by mishandling the TerrainInfo, it will work flawlessly without the hassle of creating it with a separate tool and searching for formats which are OK with being turned into G16.

If you don't understand something, if you've never used UnrealEd 3.0 for UT2003/4 or if you need more details about anything, just ask, I'll be more than happy to pour pages and pages of explanations upon your head, I love this editor.

Alright then. I don't know how similar the TerrainEditingTool in UE3/UE4 are to this one, so here are the general principles:
You crate a large empty cube to contain the entire terrain, add a zoneinfo and change bTerrainZone to true in its parametes.
Then, open the TerrainEditingTool, create a new heightmap from scratch (there's a specific button for that), with a size in powers of two. By default, each quad (set of 2 triangles) in the terrain is 64 units wide, so you usually input a size which is the size of your cube/64, but the size of the quads can be altered afterwards, so it's a matter of how many polygons you want more than a matter of size.
Then you use the tool to add layers, decolayers and shape your terrain.
In Unreal2 you cannot create the heightmap from scratch so you have to import it. Once it's imported, you can use all the usual tools to shape the terrain, add layers and decolayers (add lights to your map first as a bug makes the terrain always display in Dynamic Light mode).

Here's a basic tutorial on how to make a map for UT2003/4. Unreal 2 works the same once you have a heightmap in. My suggestion it to make the heightmap in UT2003/4 and then import it and work on it in U2.

Any format that supports 8-bits greyscale. BMP works, but it might have trouble converting to G16 in the editor. If your image editor supports it, try pcx. Basically, any format UnrealEd accepts is fine, as long as you can set it as 8-bits greyscale.

I have a problem. When I try to search for my texture in the TerrainMap section in the TerrainInfoProperties the editor crashes. 

Umm... Am I suppose to be able to see the heightmap once I select it in the TerrainMap field in the TerrainInfoProperties and build the map? Cause nothing is appearing. 

Damn! I already saved it into an existing package and it wont let me delete it from that package either. Says it is still in use even though I removed it from the TerrainInfoProperties.

Imported it again in Package 'MyLevel'. Also how do you use the texture once it is saved in the 'MyLevel' Package? Been trying to figure it out for a while, esp within the TerrainInfoProperties.

I think I am having serious problems with the generic browser. I tried just to import into a new package and save it using this guide:

https://wiki.beyondunreal.com/Legacy:Learn_The_Tools#Save_yer_Package

And it still wont work. Both methods don't seem to work. It is like the generic browser isn't registering that I want to import a texture into a new package or in the map itself. It is driving me insane.