It is done through SSLContext. You init one and then use it's socket factory to create HttpsConnection instances.
Here is rough example of how I manage this in my application:
SSLContext sc = SSLContext.getInstance("SSL");
sc.init(myKeyManagerFactory.getKeyManagers(), myTrustManagerArray, new java.security.SecureRandom());
HttpsURLConnection.setDefaultSSLSocketFactory(sc.getSocketFactory());
after that your openConnection() calls for https sites will use the sslsocketfactory you initialized here.
Here code for TrustManager to use in your ssl context wich will trust all certificates:
TrustManager[] myTrustManagerArray = new TrustManager[]{new TrustEveryoneManager()};
class TrustEveryoneManager implements X509TrustManager {
    public void checkClientTrusted(X509Certificate[] arg0, String arg1){}
    public void checkServerTrusted(X509Certificate[] arg0, String arg1){}
    public X509Certificate[] getAcceptedIssuers() {
        return null;
    }
}
Upd from Bruno: beware, trusting any certificate, however convenient it is, makes the connection vulnerable to MITM attacks