Honestly, the best advice I can give you is good luck. It took me 7 months to find work here in BG as an English teacher. Some people find work quicker, some slower. The biggest problem is that fact that you'll need a visa. 80%, if not more, of the language schools here are not big on giving work visas. The taxes are a bit extreme for them, so I can't blame them.
The schools will be hiring VERY soon. So you'll have to be calling many language schools. Do not attempt email as they rarely check or reply back to email. I would honestly suggest you come to BG asap and visit schools in person. However, if you don't find work within about 45 days you'll need to prepare to head back home. To apply for a work visa you have to have everything submitted 30 days before your 90 day tourist visa is up. I assume you're a UK citizen, so you have 90 days in Serbia, visa free. After that you have to be to gone for another 90 before being able to enter again. Ideally, you'll need to find work, and the visa paperwork submitted by day 60 of your 90.
Also, try this site: belgradefvc.com and ask about on the forum.
Good luck!!
Cao,
Kiki
