I can't resist a good meme, thanks @kalgrl for starting and others for getting on the bandwagon.
While I was finishing my Graduate Diploma at Curtin University in 1993 I picked up my first professional job as a librarian (technically not quite professional as I wasn't yet graduated but I still claim it as my first real librarian work - I got PAID for it). I responded to a request from Jennie Barwick, then a part time librarian at the Crime Research Centre at UWA, for someone to undertake a small project to establish a database of serials using INMAGIC. There was about 30 hours work.
I knew nothing about serials, nothing about databases and nothing about INMAGIC but I applied and got the work.
Carol Newton-Smith was fond of saying (when I worked with her) 'bite off more than you can chew and chew like crazy'. I 'chewed like crazy' - learned what I needed to know and got through the contract unscathed.
If I was to give advice to new library graduates, then it would be that no job is too small or too temporary. I went from this job to another short contract for Kerry Smith, to a 3 month fixed term contract in the Curtin library and eventually onto an ongoing position. Each job helped me develop some skills, connect to library people (future employers) and have something to write in my resume.
I also like that my first paid work was about discovery, a work that is as relevant today as it was in 1993.