How do I connect to a specific Wi-Fi network in Android programmatically?

You need to create WifiConfiguration instance like this:

String networkSSID = "test";
String networkPass = "pass";

WifiConfiguration conf = new WifiConfiguration();
conf.SSID = "\"" + networkSSID + "\"";   // Please note the quotes. String should contain ssid in quotes

Then, for WEP network you need to do this:

conf.wepKeys[0] = "\"" + networkPass + "\""; 
conf.wepTxKeyIndex = 0;
conf.allowedKeyManagement.set(WifiConfiguration.KeyMgmt.NONE);
conf.allowedGroupCiphers.set(WifiConfiguration.GroupCipher.WEP40); 

For WPA network you need to add passphrase like this:

conf.preSharedKey = "\""+ networkPass +"\"";

For Open network you need to do this:

conf.allowedKeyManagement.set(WifiConfiguration.KeyMgmt.NONE);

Then, you need to add it to Android wifi manager settings:

WifiManager wifiManager = (WifiManager)context.getSystemService(Context.WIFI_SERVICE); 
wifiManager.addNetwork(conf);

And finally, you might need to enable it, so Android connects to it:

List<WifiConfiguration> list = wifiManager.getConfiguredNetworks();
for( WifiConfiguration i : list ) {
    if(i.SSID != null && i.SSID.equals("\"" + networkSSID + "\"")) {
         wifiManager.disconnect();
         wifiManager.enableNetwork(i.networkId, true);
         wifiManager.reconnect();               

         break;
    }           
 }

UPD: In case of WEP, if your password is in hex, you do not need to surround it with quotes.