Bangkok is incredibly well-connected to other major cities and airports around the world. The city has two airports: Suvarnabhumi, the main international airport, and Don Muang, which mostly services smaller budget airlines.
Coming from anywhere within Thailand is even easier, as most places around the country have direct bus and train lines to the city. Domestic flights through airlines like Nok Air or Air Asia are very affordable as well. If you book far enough in advance, you can reach Bangkok from places like Chiang Mai for as little as $30 USD one-way.