The Medici had branches in: Madrid, Rome, Paris, London, Florence (obviously), Pisa, Milan, Venice, Geneva (which moved to Lyons in 1466), Avignon, and Bruges. There was also a branch that followed the Pope around.
Assets-Nongovernmental
For the bulk of their non government assets, they didn't charge interest, but rather took advantage of exchange rate shifts, selling bills of exchange for currency to be delivered at a later date.
Let's look at 1 hypothetical transaction: a merchant from Florence conducting trade in London.
(1) the merchant obtains credit from the Medici's to buy goods in Florence. The medici's have loaned cash (- assetB, +cashM) and obtained an IOU (assetB, liabilityM); (2) merchants acquires a bill of exchange on currency; (2) merchant buys goods (-cash, +inventory); (3) merchant goes to London (-cash); (4) merchant sells goods (+cash, -inventory); (5) merchant cashes repays loan (-cashM, +cashB).
However, English currency is different than Florencian currency. So, the merchant is selling goods for pounds and buying them in florins. The Medici's are loaning florins and being repaid in pounds. If the exchange rate rises (1 pound buys more florins), the Medici made money on the transaction.
They would also sell bills of exchange denominated in pounds at a specified exchange rate. So, the merchant obtains a contract from the Medici that he will receive pounds in London.
The Government Assets:
However, the Medici also made loans to government on security of tax revenues. This presented a political issue though: what stops the government from reneging? There were other banks who could make loans, buy office, etc. To mitigate this issue, they formed a cartel alongside other banks. If the governments did not repay, or did not work with the bank in case of non-repayment, nobody in the network would make loans to that government. This was obviously an undesirable outcome for the government. However, sometimes the government still did renege, or settlements were less than the original loan, to mitigate against this possibility, oftentimes banks would jointly make loans and underwrite each other's loans accomplishing two things: (a) insuring against risk; (b) strengthening the cartel.
Overall, they avoided usury laws by not engaging in usury (at least for the bulk of their transactions.)