First notebook entry: Introducing myself

Hajimemashite, Heike van den Bergh degozaimasu(to-moushi-masu, desu). Koko <strike>ni</strike>de watashi no nihongo wo motto yoku <strike>ni suru no ga</strike> shitai to omotteimasu. Doozo yoroshiku onegaishimasu.

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・"desu" is casual. "to-moushi-masu" is polite. And "degozaimasu" is very polite, like the situation that hote staff attends customer. I think "desu" or "to-moushi-masu" is just suit to these usual convasation.

・ni=to(eng.), de=in, at (eng.) 

・yoku-shi-tai=want to improve

I can almost understand your sentence as it is. And you spell Japanese words very correctly. It's good work. 
Do you know how to set up Japanese input system on PC? If so, it's better to write with hiragana and katakana.

First notebook entry: Introducing myself

Hajimemashite, Heike van den Bergh to mooshiagemasu. Koko de watashi no nihongo wo motto yoku ni shitai to omotteimasu. Doozo yoroshiku onegaishimasu. Watashi wa nijunen mae ni Nihongaku wo benkyo shimashita, Bonn Daigaku de to Waseda Daigaku de. Ryugakusei yori Waseda ni imashita. Natsukashii! Ima wa daishinpai shimasu sonso jisshin to tsunami no wake de... Watashi no Nihon no tomtodachi to zenzen renraku ga dekinai - denwa de to email de kotaemasen.

First notebook entry: Introducing myself

Hajimemashite, Heike van den Bergh to mooshiagemasu. Koko de watashi no nihongo wo motto yoku ni shitai to omotteimasu. Doozo yoroshiku onegaishimasu. Watashi wa nijunen mae ni Nihongaku wo benkyo shimashita, Bonn Daigaku de to Waseda Daigaku de. Ryugakusei yori Waseda ni imashita. Natsukashii! Ima wa daishinpai shimasu sonso jisshin to tsunami no wake de... Watashi no Nihon no tomtodachi to zenzen renraku ga dekinai - denwa de to email de kotaemasen.