Pilot Keeps Going Out
The biggest reason a Coleman furnace pilot light keeps going out is the thermocouple is placed too far from the pilot light. The thermocouple is a sensor inside a steel sleeve that sits in front of the pilot light. The pilot light must heat the thermocouple so the thermocouple can keep sending an electrical charge back to the furnace, which keeps the gas valve from shutting closed. To that end, the pilot light should be adjusted so the flame it gives off is at least two inches long. Should it still keep going out, the thermocouple is faulty and needs to be replaced.
Insufficient Heat Provided
Try raising the thermostat by a few degrees. If this doesn't help, make sure that the warm air coming from the furnace is actually going throughout the home by cleaning the air filters and making sure all the vents in the house are open. Should this not help, then there are only two other possible causes of the problem: the burners are dirty, or the blower motor's fan belt isn't working. Dirty burners can only be cleaned by a professional, so leave that for the last possibility. Open the access panel of the Coleman furnace and look for the blower motor at the base. A belt should connect it to a fan assembly. Look the belt over, it may need to be tightened if it's loose, or replaced if it's frayed.
Furnace doesn't run
Check the fuse box or the circuit breaker to make sure that power is getting to the furnace. Next, make sure that the power switch on the Coleman furnace is in the "On" position. The motor could be overheated, though this will typically only happen if it's been running in excess of several hours already. Leave it for half an hour before starting it again. If it still won't start, check to make sure your pilot light is burning. Re-light it if you must. Should the pilot refuse to light, check to make sure the gas valve to the furnace is completely open. This covers all the basics. If the furnace still won't run, call a professional Coleman furnace repair representative for diagnostic tips.