I am renting a home that is 50 years old. It has recently turn cool, low 30s. If I turn the heating/air switch to heat and 70 + degrees. All I get is cool air coming out of the air vents.

Can someone tell me what things I should do before calling heating specialist?

System may have pilot it depends on how old system is
Look at gas valve if you see the word pilot on valve and compress knob when in pilot position it will have to be lit
If you see a ignitor type device which will usually have wires for device to gas valve it's a glow cell or intermitent type pilot meaning electrical type
Newer systems use glow ignitors or spark for pilot you may have instuctions located on heater for lighting a pilot