North on the M1
Take a tram to Phoenix Park costs 2 GBP or see blackriding below. Walk north on the A road, once you pass the garage you will see signs to the M1, you can stand at the slip road of the roundabout.
South on the M1
Take the tram to Clifton South. Walk out of the station through the car park to the roundabout on the A453. Traffic flows fairly slowly here so good place for a lift to the M1 - or if you're lucky, further south.
Alternatively, you can get off the tram at Clifton centre and walk 10 minutes along Green lane to the Tesco petrol station just after the roundabout. Wait times are generally good and you can get rides to the South on the M1 or towards the Midlands/South West.
North/South on the M1
The quickest way onto the M1 from Nottingham is to go to Trowell Service Station. You can get there on the bus "Rainbow 2" which leaves every half an hour from the Victoria Centre bus station. From when you leave the built up area, count 3 bus stops and get off there. The stop is called Waterloo Lane and it's worth asking the driver if you've not been there before as the bus travels at 60 past it. The ticket is currently (July 2013) £2.60 and is to 'Motorway Bridge'. Walk up Waterloo Lane which is opposite the bus stop for 10 minutes and you're there. There is a footbridge over the motorway so you can head either north or south from here. Best place to stand is by the turn in to the BP garage.
As an alternative to the overpriced Nottingham buses it is fairly easy to thumb a lift on the A52 heading west at one of the areas to pull in after the QMC hospital roundabout. You will probably get a lift to the junction of the M1/A52. There are good slip roads with plenty of room to stop in both directions.
Most routes within the City served by Nottingham City Transport, longer routes going to the suburbs served by Trent Barton. Very centralized system with all buses starting in the not-so-big City Centre. Lots of every '10 min + services' and the Kangaroo day pass is not bad at £3.40 for all buses and the tram. Journey planner at triptimes.co.uk.
The newly built tram system can take you to the Southern and Western outskirts of the city for lifts onto the M1, a single ticket usually costs £1-2 as of November 2016. It may still be possible to blackride the tram, but security has tightened in the past year. If you attempt to blackride and see a guard at the next stop, get off. It is best to buy a ticket at this point and get on the next tram as the guards tend to get off at every stop and get on the next one, so you'll quickly be noticed.