Because the home economy is small relative to the foreign economy, we can safely assume that changes at home will not significantly affect the state of the foreign market. This is called a "small open economy" model.
If foreign income increases, its demand for goods will increase, and this includes goods that are imported from the home economy. Therefore demand for home goods will increase, resulting in money flows from outside.
These money flows will increase demand for our currency, which since the exchange rate is floating will rise in value. This will reduce money flowing in as exports and increase money flowing out as imports. When equilibrium is reached, both exports and imports should have increased, increasing our GDP but not changing our balance of trade.
An increase in the foreign money supply will cause inflation in the foreign economy, and also increase money flows into the home economy. Between both the increased exports and the foreign inflation, the home currency will have even more pressure to increase in value. But since the exchange rate is fixed, this can't happen. So the currency will remain undervalued.
Instead, the home economy will begin accumulating foreign reserves, and will begin to experience a trade surplus and a current account surplus. This will make the home balance sheet stronger, which may seem desirable (some economists think it is desirable in some cases), but carries four large downsides:
First, it pulls reserves from other countries, who may not be able to sustain their current account deficits indefinitely. If their deficit collapses, so must our surplus.
Second, it can trigger inflation in the local economy, which monetary policy may be insufficient to control.
Third, it means exchanging real goods for nothing more than paper, gradually reducing the real wealth of the home country.
Fourth, it introduces inefficiencies into the global trade system that reduce wealth for everyone, similar to a tariff or quota.