Demuxing MPEG2 is quite simple. You can either use Project X or PVAStrumento which I prefer.

Download PVAStrumento and install it. Start the GUI, open your recording (TS, MPG, what so ever) and click demux. Give a base filename for output, and check all three options saying something with "Cuttermaran" so you can easily cut your recording afterwards. Now click start and you're done.

Cutting DVB-T recordings is simple. If the recording is a MPEG2 transport stream (file ending .ts), you have to either convert or demux it.
If your just have MPEG2 Audio and Video, you can convert the transport stream to a MPEG2 program stream (PS, file ending .mpg) as described in this article and then cut it using TerraTec Cut!. That's it, you don't have to read any further.
If your recording contains AC3 audio streams you want to keep, you have to demux it to MPEG2 Video (.m2v), MPEG2 Audio (.mp2 or .mpa) and AC3 Audio (.ac3). See this article and then continue reading.

Open your video file(s) with Cuttermaran. Perhaps you have to open additional audio files if they are not automatically recognized. To use inter-frame cutting you have to configure a MPEG2-Encoder. I am using the free QuEnc, which you have to configure under Actions > Settings... > Encoding.
Navigate to the begin of the film and use the I-, P- and B-Controls to finetune. Click cut in. Navigate to the end, finetune and click cut out and then + to add the range to the cut list.
When done, click Cut audio and video to open the output dialogue. Specify the output path and change to the Mux tab. Choose any muxer you want and select the desired format. MPG or "Generic MPEG2" creates a standard MPEG2 file to play on your computer. Or create a DVD/VOB which you can directly burn, author or shrink. Start the process with Cut & Close.

Here are some choices how I do this depending on what I am trying to achieve.

1. Simple cut and storing as MPEG2 file
2. Exact cut and storing as MPEG2 file
3. Exact cut and authoring a DVD

1. Simple cut and storing as MPEG2 file

I am assuming the record is a MPEG2 program stream (PS), the file has the ending .mpg. If you have recorded a MPEG2 transport stream (TS), where the file ending is .ts, read the article how to convert it to a program stream first.
Now, open it with the freeware TerraTec Cut!, which is included in the Home Cinema installation. Let it scan the file, mark all ranges to be included in the cut file and cut it. Finished!

2. Exact cut and storing as MPEG2 file

Download and install PVAStrumento. Start it, select the recording (either .mpg or .ts) and click demux. Enable all three checkboxes for Cuttermaran and start the demux.

Download and install Cuttermaran and the free MPEG2 encoder QuEnc. Start Cuttermaran, open the settings (Actions > Settings...) and change to the Encode tab. Enable encoding, select QuEnc and configure the path to the QuEnc.exe.

Open the files (yes, there might be multiple files!) you want to cut in Cuttermaran, each in it's own Video tab. Add additional audio files if cuttermaran did not autoload them.
Select the ranges (in order!) you want to have in the result cut file using the timeline below and the I-, P-, B-Buttons at the left side. Add the ranges.
When done, select Cut audio and video, configure the output path and start the cut.

Download and install the ImagoMPEG-Muxer. Select input video and audio files, the desired output format and path and start muxing. Additionally you can configure Cuttermaran to use ImagoMPEG-Muxer to auto-mux after cutting.

3. Exact cut and authoring a DVD

First cut your record using the steps above, but do not multiplex the resulting files at the end.

Download and install GUI for dvdauthor. Start it, browse in Source to the video file and drag it onto the empty menu. Add the audio tracks and set the according language. Create chapters using the Visual Chapter Editor. Additionally, you can create chapters in Cuttermaran before cut, advise Cuttermaran to create a text file for dvdauthor in the cut dialogue and open that file here.

Right click onto the newly create text button to edit it. Doubleclick it to go into the title menu where you can set the chapters. Mark a chapter in the chapter list, and click Insert > Chapter Button and then click into the preview window. Right click to edit. If you were using the Visual Chapter Editor to create chapters, you were able to create images or short clips for each chapter. These will be automatically inserted, too.

Now configure the output. Open the Settings (no matter which) and configure output directory and check Create ISO and tick ImgBurn. Switch to the Permanent tab and enter a volume name for the DVD to be created. Close the settings.

Create your DVD image by pressing Create DVD. Now you have an ISO image that you can burn to a CD or DVD.

I have some DVB-T recordings made as a MPEG2 transport stream (file ending .ts). Unfortunately, the latest version of TerraTec Cut! cannot handle these. It just loads them, scans until the end of the first video (in most cases there are multiple videos contained in the stream) and then won't do anything more. So I was looking for a way to convert these to the "standard" MPEG2 program stream (PS) with file ending .mpg which Cut! handles without any problem.

Download and unpack PVAStrumento. Start the GUI, open the .ts-file and click make ps. Name an output file and and press start.

Now you will have a single mpg-file for each of the videos contained. Just delete the files you do not need, e.g. adverts, previews etc and you are finished.