There are three important things when writing Japanese, whether it be kana or kanji:
Stroke order
Every character has a set way of being written and the strokes have an order to them.
For example, when we write 木, we first write the horizontal stroke, then the vertical and then the left sweep and right sweep.
Try to follow this stroke order and memorise it. It might look arbitrary and daunting at first, but after the first few hundred kanji you will realise the pattern and be able to guess the stroke order of kanji you don't even know yet.
Is stroke order important? Yes, it is. It's the most efficient way of writing (even if it may not look like it to the untrained eye) and brings consistency to your writing. It becomes especially important when writing (and reading) in 行書 "semi-cursive" which relies on the right stroke order.

Character Balance
Do not copy computer fonts.
The characters you see on the screen look the way they do mostly because they are made to fit in a tiny block with a limited set of pixels.
However, this is not how we actually write the characters.
Some examples of this are:
- We don't connect き and さ
- We don't put the dakuten ( ゙) in the middle of a character like in で, but always at the top right
- We don't write 入 like... that
You can compare this to how we don't write a Times New Roman "g" when handwriting in English.


Proportions
Proportions are also very important. In order to practice character balance and get used to it, it's highly advised you write each character in a box divided by a 4 section grid, like so: 田
You can then look up stroke order and proportions of each kanji on for example Jisho.org
You can download practice sheets or make them yourself. You can also just buy any grid notebook as long as the grid isn't too small and you can write a single character in 4 squares comfortably.
As a last resort you can also simply draw a grid yourself.

Types of strokes
There are 3 basic types of stroke endings:
- とめ or "stop"
- はね or "jump" (or hook, flick, etc)
- はらい or "sweep" (or brush, etc)
These apply to kana as well as kanji, just like everything else that's written above. This image should explain the difference:

Where to start?
As for where to start, start with learning how to write hiragana properly: