LHR Terminal 3 to Terminal 4

Airside or Landside? That is are you trying to get to a connecting flight or are you trying to get to another terminal after you arrive in London and go through immigration, baggage claim, and customs?

Thank you for your reply, & sorry for not including important info. Landside, and I'm not connecting. What I'm trying to do is get from T3 to the Hilton located at T4. I'd been busy searching info on the LHR website, and also the hotel website when you replied to my topic. This is what I found: One option is to take the Heathrow Express from T3 to T5. I'm familiar with this, as I did it last month. Then from T5, take the hotel shuttle to the Hilton. The bus picks up passengers about 30 minutes. However, my husband is not interested because of the 30 minute intervals. The other option is the one he thinks we are interested in, but I need clarification, please. I found that the website said to take the Heathrow Connect/Heathrow Express from T3 to T4. Then there is a covered walkway from T4 to the hotel. It appears that the train arrives every 30 minutes.
And there isn't a clue as to how long the walkway is in distance or time. Which option is best? Thanks.

Okay, I figured out how to get from T3 to T4 via the free train. So my question now is how far is the walk from T4 to the Hilton? Thanks again.

Unfortunately, I've never stayed at the Hilton so haven't made that walk myself. The hotel itself is not far from the terminal, so I can't imagine it would be more than 10 minutes. Hopefully someone who has stayed there can give you a better estimate. Regardless, I think taking the train to T4 is your best option and will involve the least amount of walking overall.

An alternative (not necessarily recommended) is to take a bus to Hatton Cross from Heathrow Central Bus station and one from there to T4 / Hilton. Would still be free. The Heathrow Connect service runs up to four times an hour though between T1,3->T4 - but only two of these then carry on into London.

Here's a link that shows you exactly how to get there.
http://www3.hilton.com/en/hotels/united-kingdom/hilton-london-heathrow-airport-LHRAPTW/maps-directions/index.html