Gatwick to Covent Garden - easy directions?

Looking at Google Maps for this coming Sunday around 4pm, it looks like the easiest would be the Thameslink to St Pancras station. Then you just follow the signs to Kings Cross Underground station, which is just across the street, and take the Picadilly Tube to the Covent Garden stop.

There are lots of YouTube videos to show you how to ride the trains and Undrground. Both the trains and tubes announce the next stop as they approach. Every tube car has a map showing all the stops, so you can see where you are and how far to your stop.

The above is fundamentally correct except the underground station is Kings Cross St Pancras (one tube/underground station serves two railway stations) so you don't have to cross the street.
You transfer undercover within St Pancras station following the signs. Basically Thameslink (which runs literally 24/7) uses sub surface platforms at the north end of St Pancras. So come up the escalators to the main station, then walk the full length of the station past Eurostar to the South end of the station where the tube/underground is.
What needs to be checked is whether the line is closed by Sunday engineering work.
EDIT- The above applies on 14, 21 and 28 September. On 7 September Thameslink terminates at London Bridge with no cross London service.

The easiest route would then be by taxi.

However you could change at London Bridge onto a Charing Cross bound train then one stop on the tube (Northern Line) to Leicester Square. Leicester Square and Covent Garden stations are exceedingly close to each other so your hotel will be a very short walk from Leicester Square. Easier than changing tube line one stop to Covent Garden.
FURTHER EDIT- As your hotel is the Seven Dials Hotel then Tottenham Court Road station is slightly closer than Covent Garden station, so on 7 September go 2 stops on the Northern line from Charing Cross to TCR.
On the other Sundays I might contemplate the easier change from Thameslink to the Elizabeth Line (westbound) at Farringdon, one stop to TCR.

The information from Google Maps above is not how I would do it. Charing Cross is much closer to Covent Garden than Kings Cross is. We just did this exact trip. The correct route is a Southern train from Gatwick to London Bridge; then connecting to a Southeastern Train to Charing Cross. Most of Covent Garden is within walking distance of Charing Cross, but if not you can use a cab, tube or bus.

Both trains run very frequently. You can pay by simply tapping a contactless card at Gatwick (don't forget to tap out at Charing Cross).

The trains from Gatwick to London Bridge are run by Thameslink, not Southern.
In any event your hotel is much nearer Tottenham Court Road than Charing Cross. For me the easiest route is Thameslink to Farringdon and Elizabeth line to Tottenham Court Road.

The trains from Gatwick to London Bridge are run by Thameslink, not Southern.

Correct. My typo. Southern trains go to Victoria, not London Bridge.

I don't know if it's useful for you to get more opinions, but my preferred way for getting from Gatwick to Seven Dials would be Thameslink to Farringdon and Elizabeth Line to Tottenham Court Road, as others have mentioned above.