Reaching Gulmarg is no challenge and can be reached by various routes. If you are coming from another country or city, you are to reach Srinagar (Capital city of Jammu & Kashmir) first by
Air: Srinagar airport is frequently connected to New Delhi (the national capital). As many as 14 daily flights fly to Srinagar from New delhi and the ride time is only a matter of 90 minutes.
Train: Trains to Jammu are easily available from the rest of the country. Once in Jammu you can get to Srinagar by taking the bus or hiring a cab or jeep. The road distance from Delhi to Srinagar is 24 hrs.
Once you have successfully arrived at Srinagar, Gulmarg is very close to it. You can choose to go to Gulmarg by bus or by car from Srinagar. The road journey would be of about an hour (depending on the weather conditions).
You can also hop onto a SRTC coach that will take you for a daily sightseeing tour and get down at the Gulmarg Gondola. The Tourist Reception Centre is where you need to go to get onto the sightseeing coach.
If you want to take the local transport, then buses are available to take you to the Tangmarg (a village close to Gulmarg) market. From the market mini coaches are available upto Gulmarg. Private taxis are also readily available from the taxi stands. You will be charged for wither a fixed one way price or for a return journey.
From Gulmarg to Gulmarg Gondola, you can either take a private jeep, taxi, horse ride or a walk.