The Pasuk regarding the Misva of Sisit states, "Gedilim Ta'aseh Lach"- You shall make strings for yourself. The Rabbis derive from the words "for yourself" that the "T'viyah" (spinning the strings from the raw wool) must be done "L'shem Misva"-with the express purpose of fulfilling the Misva. The Shulhan Aruch (Siman 11) rules that it is not sufficient that this intent be thought mentally, it must be verbalized. However, if a person declared the proper intent in the beginning of the process, it is not necessary to constantly repeat it throughout.
The Mishna Berura (R. Yisrael Meir Kagan, Poland, 1839-1933) discusses a case in which a person began the process of spinning the strings without having intent for the Misva and subsequently declared the proper intent in the middle of the process. He rules that such strings are Pasul (invalid). We do not say that since he finished with intent for the Misva that he also began with it.
However, if he started the process with mental intent for the Misva and only subsequently verbalized his original intent, the Mishna Berura rules that the strings are Kosher, as there is a "Safek Sefeka" (double doubt) to be lenient.
There is a major debate amongst the Poskim whether the strings can be spun by machine, with intent by the operator to produce strings for the Misva. Hacham Bension ruled that it is not possible to have intent for the Misva with a machine, whereas Hacham Ovadia ruled that it is valid. Since today strings that are "Tviyah L'shma- Avodat Yad" (Hand Spun for the Sake of the Misva) are readily available, one should make an effort to purchase them and avoid the controversy. However, if someone already has Sisit spun by machine, he may rely on Hacham Ovadia.
SUMMARY
The strings of Sisit must be spun for the purpose of the Misva. This intent must be verbalized. If a person began, only thinking the intent mentally, but later verbalized it, the strings are Kosher. However, if he only began to have intent once the process was underway, the strings are invalid.
It is best to use strings spun by hand.