I don't think you can enter into yahoo directory free of cost. You can be recognized by the yahoo as search engine but no free inclusion allowed. You have to pay a hefty fee for inclusion and if your site is not considered for inclusion, the fee paid is non refundable
If you pay, it can happen immediately. The free one could take forever, and sometimes they never come around. I know people that have had sites for a long time and aren't anywhere in yahoo.
There is no yahoo directory for Free. Only NON-profit sites and non commercial sites can get listed for Free.
$299. Takes (based on my experience this week) about 2-3 days to get your listing processed. I am just ashamed to admit this, but I submitted three sites (forgetting that late last year I'd already submitted one)... and, yep, you pay the $299 just for submitting. So I paid $299 three times. Got two sites listed.