There are direct flights to Inverness Airport from London (Heathrow, Gatwick & Luton), Amsterdam (Schiphol), Bristol, Manchester, Birmingham, Dublin, Belfast, Zurich … https://www.invernessairport.co.uk/fly-direct/
The airport in Inverness (like most airports) is a bit out of town. There are busses to get you from the airport to the city center and back. “The bus fares to and from Inverness Airport are around £3.10. Getting to by bus from the bus station to Inverness Airport takes around 30 minutes.” https://www.invernessairport.net/transport/buses.shtml . You will need cash – in Pounds – to pay for the bus. You can also take a taxi. Here is more information: https://www.invernessairport.co.uk/to-and-from-the-airport/
Bus or Train
If you want to take a bus or train from Glasgow or Edinburgh, they will drop you off right in the center of town. Here is a map with the bus station the train station circled and the Inverness Castle underlined so you can see where they are in relation to the castle. Click on the map to enlarge.
I use https://www.thetrainline.com/ to look for train tickets. For Glasgow, you would leave from Queen Street station. For Edinburgh, you would probably want to leave from Waverly station, but possibly Haymarket if you are staying further out. Please see these blogs about getting around Glasgow, Edinburgh and between them:
Blog Link (opens in new tab): Getting Around Glasgow
Blog Link (opens in new tab): Getting Around Edinburgh
Blog Link (opens in new tab): Getting between Glasgow and Edinburgh
Click on the map to enlarge.
Or there are buses from almost anywhere in Scotland. Here are some bus links:
I use google maps, put in the destination, then press the Directions button. Then you can add an Origin and select the thing that looks like a train.
If you’ve taken the ferry from Belfast to Cairnryan (Stena Line Ferry), then you can take the bus from Cairnryan to Ayr then the train to Inverness.