What was the unions strategy they put in place in order to win the civil war?

On the outbreak of hostilities, the elderly General-in-Chef, Winfield Scott, declared that it would be a long war, and that the first year should be spent blockading the Southern ports, to starve the Confederacy of food and war supplies. After that, there would be a drive down the Mississippi, and only then an offensive campaign of large armies.

This plan was ridiculed as the 'Anaconda' (slow strangulation), because everyone else thought it would actually be a short and bloodless war.

Later, when they found they were wrong, they did put a similar plan into effect.

When Grant was promoted General-in-Chief in March 1864, he effectively carried out slow strangulation by ending the system of prisoner-exchange, and then just watching the Confederates run out of manpower.