Train

I'd suggest starting with the The Man in Seat 61 website to familiarize yourself with UK trains -- https://www.seat61.com

As for train operating companies LNER operates part of that route and Northern operates part of it too. You can buy your tickets for the journey from either company. You can get your tickets from any train operating company for that matter -- https://www.lner.co.uk/ OR https://www.northernrailway.co.uk/

One caution to pay attention to is that Bradford Interchange is the other station and some ticket options have that as the arrival station.

Much of the timetables start the journey from London Kings Cross, so you'll want to travel from LHR to Kings Cross.
Direct can be accomplished on the Piccadilly line from LHR to Kings Cross on the tube in a hour journey time. Indirectly By Heathrow Express or the Elizabeth Line.

Take the Underground from Heathrow to London Kings Cross station

Trains from London only go to Bradford Interchange station. Forster Square is a 10-minute walk away.

You can book train tickets from Kings Cross to Bradford Interchange here https://www.lner.co.uk/

I'm sitting here looking at a random day and If I wanted a train to Bradford forester Square, that option provided by LNER would be Kings Cross to Leeds change at Leeds to Shipley, change at Shipley to Bradford Forester Square.

A journey to Bradford Interchange tends to be the one change at Leeds.

But journeys are available to either Bradford station from Kings Cross.

Thank you all for the great information

It is Forster Square.

All direct trains from Kings Cross to Bradford Interchange are run by Grand Central Trains, although they will show on LNER and can be booked through LNER. You need to look at the journey details to establish that.
They can also be booked through the Grand Central website.
These are the direct trains-
https://www.grandcentralrail.com/travelling-with-gc/timetables
Every other LNER train to Leeds has a connection to Interchange on Northern Trains (as a through fare). When you get to Leeds you will be looking on the destination board for a train to Manchester or Blackpool as that is where the train is heading to. No Northern train on that route runs only to the Interchange.
If you want to go to Forster Square you don't want to mess round with changing at Shipley- that is a confusing station with platforms on 3 sides of a triangle, with trains running in all sorts of directions
Catch a LNER train to Leeds then at 12 and 42 minutes past each hour there is a direct train to Forster Square. That is it's terminus so is much easier to find on the destination boards. Those trains are also much quieter than the ones to the Interchange. That will stop at Shipley but you don't change there.

By the way I have just noticed there seem to be a lot of peculiaritys in the through fares.
Be very careful when you book not to pay more than you should.
You should be able to book a through fare to Forster Square from around £22.50 to around £43.
If you are quoted more than that check what the fares are to Leeds.
On certain dates only the 3 minutes past each hour are showing cheap fares to Leeds, the 33 past showing £125. If you see that travel on the 3 minutes past train.
On other dates there are cheap fares to Leeds, but not to Forster Square.
If that happens then book a fare to Leeds, then a 2nd ticket from Leeds to Bradford which costs £4.90.
On no account pay £125 or anything like it, on some dates I can see fares as high as £145 on off peak trains.

Yes it is Forester square not the interchange

I've just been checking the printed timetables to find the only through trains each day to Forster (NOT Forester) Square. Forster is the correct spelling.

They run at 1633 and 1833 from King's Cross and arrive at 1929 and 2129.

Right, we get the spelling. Do you think that maybe auto correct might be a cause?

@ VAP- auto correct may or may not be the cause, but then I was using a laptop where I am not plagued by auto correct, rather than a mobile device.
I don't like to beat people round the head about spelling errors. They happen, so I was subtle, as is my style. However when the OP then repeated the mistake I was then a bit less subtle, as it suggested he had either not read or disagreed with my subtle correction. I had even checked the A-Z in case Bradford has a Forster Square where the station is, and a Forester Square elsewhere- and the OP was trying to reach the latter.
I actually know the local train network, I have used it a lot so could recognise that the earlier responses were not entirely correct. In particular I have changed (too many times) at Shipley on local trains when that is not an option. Even I get confused there, I can only imagine what it would be like to a newbie. Notwithstanding what the journey planners say I have the experience and knowledge to be aware that changing there on a long distance journey is never correct and to know of the local Leeds to BFS shuttle trains- and how long they are and their load factors.
I wasn't planning to give fare information. But after this query I looked quietly at another thread concerning the use of the trainline to book European rail tickets. And I just looked out of interest at fares on the trainline for this train journey. I was shocked to see that for this journey the trainline were saying to split tickets on every journey on this route. My fares knowledge is more than sufficient to both recognise that that is total nonsense, but also to see that by splitting tickets they are charging well over the correct fare. So I did a few sample checks to prove that theory. The trainline is not a charity, they are a profit making company. They profit from people's lack of knowledge. I can't comment on what they are like for European railways, fares wise, only on their UK performance,
Unfortunately those checks also found the discrepancies highlighted in the directly booked fares as well.
A true case of 'Caveat Emptor'

Stuggling there isn31c :-)

OP: Is there any reason you want to go to Forster Sq as opposed to Interchange? There is only a mile or so between the two stations. Onward travel will be far easier from Interchange such as snagging a taxi or bus and its a cock's stride from the centre of Bradford.

Grand Central operate 3 direct return services from Kings Cross to Bradford Interchange. Grand Central are likely to offer the cheapest fares and have the far superior trains with more leg room and a higher proportion table seats and have the highest satisfaction ratings of all the UK rail operators.

As already hinted at, it is sometimes cheaper to go to Central London and starting the train trip from there, than it is to go from Heathrow to Reading (or somewhere your train stops). So just be careful of that.