Train from Edinburgh to Inverness?

Trains run almost every hour, on alternate hours you change at Perth onto a train which has started from Glasgow.

They start from Waverley station in the City Centre at the end of Princes Street, and call at Haymarket in the west end of the city.

Which is more convenient depends on where your hotel is.

The direct trains (the ones where you don't have to change at Perth) are at 0837, 1033, 1330, 1633, 1733 and 1939. (The 1633 is a train which has come all the way from London Kings Cross so is the longest train of the day).
Except the 1633 trains are between 2 and 5 coaches long, and have a trolley service for refreshments (including alcohol)- cold food such as sandwiches and biscuits. The 1633 has a catering coach with hot food. When you buy a ticket you are allocated a seat,
but can choose window or aisle, and a choice of airline style or around a 4 seat table, and facing direction of travel or backwards. You will see the coach numbers on the outside of the coaches, and the seat numbers on the displays above each seat.
To buy tickets (normally available 12 weeks before travel, but presently only until Easter for some reason) use the Scotrail (the train operator) website.
Advance fares start from £12.90 on certain trains (normally the 0837 and 1939) or £18.30 on the other trains.
There is no clear benefit to which side of the train you sit on as the scenery swaps and changes and is often on both sides.
At least today all the above trains are 5 coaches long except the 1633 which is 9 coaches, and the 1733 which is 3 coaches.

Inverness Station is also right in the City Centre so your hotel should be in walking distance but taxis stop outside, and the bus station is adjacent.
https://www.scotrail.co.uk/

Trains run from Edinburgh Waverley at the end of Princes Street and Haymarket (in the west end of the City) to Inverness (which is in the City Centre). Every other train is direct, the others you change at Perth into one which has come from Glasgow.
So get a direct one for ease.
They run at 0837, 1033, 1330, 1633, 1733 and 1939. All are between 2 and 5 cars long (today all are 5 cars long except the 1733 (3 cars) and the 1633 (9 cars).
They are run by Scotrail except the 1633 (run by LNER, which has come from London Kings Cross).
Buy tickets from them - https://www.scotrail.co.uk/
Fares start from £12.90 on the 0837 and 1939, or £18.30 on the others.
At booking you choose an aisle or window seat, airline style or in a bay of 4, forwards or backwards.
There is no clear benefit to which side as the best scenery swaps and changes round.
All trains have a trolley service of sandwiches, biscuits and hot and cold drinks (including alcohol), the London train has a full buffet including hot food and a full restaurant car. For extra comfort and space all trains also have 1st class at a higher price.
Bookings usually open 12 weeks ahead, although currently only open until Easter. Prices increase up to £50 with time.
Your coach number is on the outside of each car (a letter actually, not number, like A to K), the seat number is above each seat,

Inverness is walkable to most hotels, but taxis are available outside, and the bus station is adjacent.
On the trains and at the stations restrooms are available.
Departure times from Haymarket are about 3 minutes later than the Waverley times given above.
There are very many options at Edinburgh Waverley to eat before the train (eat in or take out) and supermarkets in the station to buy picnic food to eat on the train.

I think that's all you need to know, but if not just ask.

You go to the Scotrail website and buy a ticket.

The Scotrail website for ticket purchase is the hyperlink in my 1st post above.
By the way at purchase you don't have to set up an account with Scotrail (if not, just select 'Continue as guest'), and will have the option to obtain the ticket as a physical ticket (collected from machines at the station with the same credit/debit card as you used for purchase), or in the scotrail app on your phone.
The machines are very easy to use, select the option for Collect pre-purchased ticket, rather than the option to buy a ticket for travel now, and follow the instructions on the machine.
If purchased on the app follow the instructions to activate the ticket before travel.
You will more than likely be using the platforms where you have to go through ticket gates to access the platforms (long distance platforms don't have gates). Just insert your ticket or scan it on the app and the gates will open. For a physical ticket collect the ticket as the gates open. There are wider gates for those with heavy luggage.
There are lots of overhead screens to tell you your platform number, usually given 10 to 15 minutes before departure.
There are similar gates at Inverness to exit the platforms.

Further information about Edinburgh- I have checked and all the above trains except the one from London are scheduled to use Platforms 15 or 16 at Waverley which are among the gated platforms. If there is service disruption that can change, but those are the scheduled platforms.

To give you a shorter answer than "War and Peace":

1) You catch a train at Edinburgh Waverly Station. Most are run by Scotrail.

2) Make sure you spend time looking out the window. The view is amazing.

3) You can buy a ticket directly from the Scotrail website or download the app and buy it on there.

Thank you so much everyone! It is appreciated!

There was another thread recently about the highly dodgy rail ninja. Totally to be avoided-

https://community.ricksteves.com/travel-forum/england/train-from-london-to-edinburgh-edb5be91-c3e4-485d-b6fe-e7adb167eb39