About from London St Pancras to Paddington?

St Pancras and Kings Cross are two separate stations beside each other linked by walkways and you need Kings Cross underground station. Its all signposted and also lots of staff to help you. Buy your ticket from the ticket office at Kings X underground station and tell the assistant that you want to return the same day and they will give you the appropriate ticket. Yes a circle line train and its an easy journey of about 10 minutes.

The Underground Station is called 'King's Cross St. Pancras' and you need to catch a train from the westbound platform - Circle Line or Hammersmith & City Line train going to Hammersmith. The journey time is about 10-15 minutes.
Some other answers mention the Metropolitan Line but this does not go to Paddington.

Buy your ticket in the station before boarding the train.

Yes'm, circle/ district and/ Metropolitan line.

When you go down to the underground station in Kings Cross ( it's next door, 1 min walk), you'll see where to pay!

http://www.tfl.gov.uk/
http://www.tfl.gov.uk/assets/downloads/standard-tube-map.pdf

No, it's an easy trip, if tube runs quickly, les than 10 minutes.

If you returning same day, a day travel pass might be best, but individual tickets on the day if different.

You get the Circle Line, or the Metropolitan Line from King's Cross St Pancras to Paddington (both from the same platform). It takes 10-15 minutes, and you buy a ticket at the station (at the ticket window or from a machine). You can't buy Underground tickets in advance from a website. I think a ticket costs £4, but it's a while since I needed to buy one.

Yup - Circle Line from King's Cross/St. Pancras to Paddington.

Journey time 12 minutes.
http://www.tubeplanner.com/search/result?from=King%27s+Cross+St.+Pancras&to=Paddington&go=Go

London UK 101212.1421

If you use the underground, you'll spend an age wandering around tunnels and going up and down escalators. As an alternative, consider taking the bus. Leave St. Pancras from a front entrance, cross the road [Euston Road], and wander along until you see a bus stop with 205 on it. Make sure you have change to buy a ticket before you board the bus. The journey on bus 205 will take longer than the underground (about 40 minutes) but you will at least be above ground, and if you have luggage, the bus will have storage space. It will be cheaper too.

Only John's answer above is really correct

I think it's the Circle line (check a tube map) the day ticket is usually around £7. You buy it from the underground. Google 'London Underground' and you will get maps and ticket prices.