Learn Hardcore Japanese: tukue no ue ni memotyou wo koteisimasu.

机にメモ帳を固定します – grammatically possible, but vague; “fix the notepad to the desk (somewhere on it)”.
机の上にメモ帳を固定します – clearly “fix the notepad on the top of the desk.”

In everyday speech, Japanese often adds 上, 中, 下, etc. to be more specific about where on an object something is.

What’s the difference between 上に, 上で, and just 上?

These are easy to mix up:

上に (うえに)
- Marks a location/result or a destination on top of something.
- Here it’s the place where the notepad ends up fixed.
- Example:
  - 机の上に本があります。 – There is a book on the desk.
上で (うえで)
- Can mean “on / on top of” (as the place where an action happens), but with a nuance of “on that surface, doing X”.
- Example:
  - 机の上で勉強します。 – I study on the desk.
- In your sentence we care about the final position, not an action happening on that surface, so に is better.
Bare 上 (without particle)
- Rare in isolation; usually needs a particle like に / で / から / まで to show its grammatical role.

So:

机の上にメモ帳を固定します。 – Fix the notepad onto the top of the desk.
机の上でメモ帳に書きます。 – I write in the notepad on the desk.

What does the particle に do here? Is it location or direction?

Here に is basically both “location” and “destination”:

It marks the target location where the notepad will end up fixed.
The verb 固定します implies a change of state: the notepad becomes fixed on top of the desk.

This is similar to:

壁にポスターを貼ります。 – I put a poster on the wall (lit. fix/attach to the wall).
床に座ります。 – I sit on the floor (I move to the state of being on the floor).

So 机の上に = “onto / in the position of being on the top of the desk”.

Why is を attached to メモ帳? Is メモ帳 the direct object of 固定します?

Yes. The particle を marks the direct object, the thing that undergoes the action.

メモ帳を固定します。
- メモ帳 = notepad
- を = object marker
- 固定します = fix / secure

So: You are fixing the notepad (and the destination is 机の上に).

Compare:

ポスターを壁に貼ります。 – I put the poster on the wall.
- ポスターを = direct object
- 壁に = destination / place where it ends up

Same pattern in your sentence.

Can I change the word order to メモ帳を机の上に固定します? Is that still correct?

Yes, that word order is completely natural and probably even more common:

メモ帳を机の上に固定します。
机の上にメモ帳を固定します。

Both are grammatically correct. Japanese word order is relatively flexible as long as the verb is at the end and the particles are correct.

Nuance:

メモ帳を… at the front: slight focus on the notepad.
机の上に… at the front: slight focus on where you’re fixing it.

But in everyday conversation they’re practically interchangeable.

What level of politeness is 固定します? How would the plain form look?

固定します is the polite ます-form of the verb 固定する.

Dictionary/plain form: 固定する – to fix / to fasten / to secure.
Polite non-past: 固定します – (I) fix / (I) will fix.

Other forms:

Plain past: 固定した – fixed.
Polite past: 固定しました – fixed (polite).
Te-form: 固定して – fixing; and to connect to another verb, etc.

So your sentence is in polite non-past, suitable for manuals, instructions, or speaking politely to someone.

What exactly is the nuance of 固定します compared to something like 置きます or 付けます?

These all involve putting something somewhere, but the nuance differs:

固定します
- “To fix / fasten / secure” so it doesn’t move.
- Used for attaching firmly: screws, glue, clamps, brackets, tape, etc.
- Very common in manuals, technical descriptions, or instructions.
置きます
- “To put/place (something somewhere)” without implying it’s fixed in place.
- Example: 机の上にメモ帳を置きます。 – I put a notepad on the desk. (You can easily move it.)
付けます
- “To attach; to put on; to apply.”
- Broad usage: attach labels, apply makeup, turn on devices (電気をつける), etc.
- 机の上にメモ帳を付けます sounds like “attach the notepad” but doesn’t strongly emphasize making it immovable like 固定します does.

So in your sentence, 固定します implies you’re securing the notepad so it stays there firmly.

How is 上 read in this sentence, and why? Is it うえ or じょう?

In 机の上に, 上 is read うえ.

General rule of thumb:

When 上 is used as a common noun meaning “top / above / on”, it’s usually read うえ.
- 机の上（うえ）, 箱の上（うえ）, 山の上（うえ）.
じょう is usually a Sino-Japanese reading used in compound words:
- 以上（いじょう）, 地上（ちじょう）, 屋上（おくじょう）, 頂上（ちょうじょう）.

Because here it’s a simple “top of the desk,” it’s うえ.

What’s the nuance of メモ帳 compared to just メモ or ノート?

メモ帳
- Literally “memo-pad.”
- A small notepad used for quick notes; often tear-off sheets, a little booklet, etc.
- Matches “notepad” or “memo pad” well.
メモ
- Broad: “memo,” “note,” or “to take a note.”
- メモを取る – to take notes.
- メモを机の上に置きます – put a note (a slip of paper) on the desk.
ノート
- General “notebook” (spiral, bound, school notebook, etc.).
- Bigger and more book-like than a typical メモ帳.

So メモ帳 makes it clear you’re talking about a small notepad-type object you might fix to the desk (e.g., with a clip, stand, or tape).

Could I add a topic marker は somewhere, like メモ帳は机の上に固定します? What changes?

Yes, you can, and it’s natural. Examples:

メモ帳は机の上に固定します。
- “As for the notepad, (we) fix it on top of the desk.”
- Focus on what you do with the notepad (maybe contrasting it with something else).
机の上にはメモ帳を固定します。
- “On the desk (at least), we fix the notepad.”
- Focus on the location, possibly contrasting with another place.

Adding は usually introduces a topic or contrast:

Without は, it’s a straightforward statement.
With は, you hint at contrast or emphasis: “as for X…”

Grammar stays correct either way; it’s a matter of nuance and context.