Praise be to Allaah.
What is meant by tawassul and waseelah is four things:
the kind of tawassul without which faith cannot be complete, which is seeking to reach Allaah (tawassul) by believing in Him and His Messengers, and obeying Him and His Messenger, This is what is meant in the aayah (interpretation of the meaning):
O you who believe! Do your duty to Allaah and fear Him. Seek the means of approach to Him
This includes seeking to approach Allaah through His Names and Attributes, or by doing acts of obedience and worship by which one seeks to approach Allaah, and so on.
Seeking to approach Allaah by asking His Messenger (peace and blessings of Allaah be upon him) to make dua for one during his lifetime, and the believers asking one another to make duaa for one another. This follows on from the first type and is encouraged.
Seeking to approach Allaah by virtue of the status and virtues of some created being, such as saying, O Allaah, I ask You by virtue of Your Prophet and so on. This is allowed by some of the ulama, but this opinion is daeef (weak). The correct view is that it is definitely haraam, because there can be no tawassul in duaa except by virtue of the Names and Attributes of Allaah.
Tawassul as it is understood by many of the Muslims of later times, which is calling on the Prophet (peace and blessings of Allaah be upon him) and seeking his help (or seeking the help of the dead and so-called awliya). This is a form of major shirk, because calling on or seeking help from anyone other than Allaah with regard to something that that only Allaah is able to do is a kind of worship, and directing worship to anyone or anything other than Allaah is major shirk. And Allaah knows best.