Car no starts?

My partner is having trouble with her car. Usually it starts first try with no problems but sometimes she has a lot of trouble before it eventually starts. It turns over and over without starting, she keeps trying and eventually gets it to start (it took her about 20 minutes yesterday when she left work). I think the problem first appeared about a month ago and has happened maybe 3-6 times in that month, every other time she has driven her car it has started ok. Are there any basic things I can check/try before seeing a mechanic? Could it be as simple as dirty spark plugs? Any other basic things I could check without a lot of specialised tools and equipment?

Thank you very much for your help and advice :)!