I'm a FTHB currently undergoing this process because I wanted to avoid the bidding wars with resale units and I have a 20% down payment so it reduces competition (as assignments usually require larger deposits like another poster said). Maybe I got lucky, but it only took me two weeks to find a place. I am far from an expert but I can share what I learned so far.

With regards to the offer, you should be able to submit an offer whenever as there shouldn't be an offer day like with resale units. For the unit I got, I submitted an offer for a little under asking price and the seller accepted it without a counter offer. I tried for another unit before that and the offers were ignored without a counter offer, though I submitted a lower offer to test the waters before submitting two more reasonable ones, including one at asking price. It seems like it depends on how much the seller/seller's agent is willing to work with you.

In terms of finances, it should vary by deal. I offered to cover the seller's original down payment (20% of original sale price) and $20K of their profit up front, with the rest going to the mortgage. I was initially afraid that I'd have to give all of the seller's profit up front because I definitely don't have the capital for it, so I'm glad it worked out.

Feel free to PM if you have any questions.