Hopefully your solicitor will be good and on it, but this is the time when you need to be prepared for lots of chasing!
Make sure alllllll the paperwork you'll need for your solicitor is in order and ready to go - any details about income, gifted deposits, etc is all in hand.
You can instruct a surveyor now - pass their details to your solicitor too, and to the estate agent handling the sale so they can sort access.
Other than that, there's not much you can do: your solicitor will start looking at paperwork and doing checks, but you can be chasing e.g. check whether their solicitors have your solicitors details yet, whether your solicitor has recieved paperwork from theirs yet and if not, chase the estate agent to get them to prompt the seller (this can go through a few rounds - e.g. we had to chase our sellers for FENSA certificates and then later something to do with the loft).
Once the paperwork is received by your solicitor, ask them what's needed from you and a rough idea when you should next hear something, and then call back if you haven't.
I'm sure any conveyancers and estate agents reading this are probably groaning internally but in my experience, you cannot assume everyone is just doing their job - we made the mistake of doing this in our first house sale and wasted 2 weeks where our solicitor had forgotten to follow something up and their side were waiting on it so nothing was happening, and it was only when we tentatively asked that it started again.
Be the squeaky wheel. Know who should have what paperwork and whether they've got it at all times and call to chase it up!
With any luck you'll have a good solicitor, though :)
Also start looking at insurance, cos you'll need that before you exchange (I think - might be before completion)!