After the problems we had had getting the visa, the border crossing was kind of anti-climactic. No hassle at all and pretty straightforward really.
We had heard that it is best to change the left over Jordan money into Syrian currency before the border, since the exchange rate is supposed to be much better. We needn't have bothered, as the exchange rate was about the same in Damascus. Also keep in mind that you will have to pay 5 JD per person and 5 JD per vehicle departure tax on the Jordanian border, so don't get rid of all your JD's!
This border crossing is very quite and so no stress was involved. First we stopped at the immigration office. We each had to fill out two entry/exit cards. On these forms they ask you how long you intend to stay in Syria. If you put down more than 15 days, the officer will remind you, that you have to register with the authorities once the initial 15 days are over. The passport and the entry/exit cards get stamped. You get to keep one entry/exit card, don't loose it you will need it when leaving the country.
Next stop is customs. First we had to take the carnet to a customs officer sitting beside a booth on the road. He basically checks the information in the carnet and asks the one very important question: petrol or diesel? If you say diesel you get hit with a very hefty (100 USD) diesel tax for every 10 days you are in the country. This "tax", is payable twice (entry and exit). Luckily with the bikes it's petrol, which means we only paid 7 USD tax per bike.
Now it was on to the insurance and tax office. There you have to buy the receipts for the insurance and the tax from the bank in the same office. As mentioned earlier you have to pay in 'hard' currency. With the receipts from the bank you can then proceed first to the insurance office and then to the tax office, where your Carnet will get stamped and registered. That's it you are free to go and are welcomed into Syria.