There is no god but God
Mohammed (sas) is the prophet of God

Allah(swt) is the Arabic word for the GOD, it is not a name given to God of Muslims as usually thought of by some non-muslims. the word Allah is used by all Arabic speakers muslims, christians and pagans etc for the God.

SWT= subbhana watala which is for Allah(swt) SAS is sallillah hu alhiwaslim which means peace be upon him and is reffered with respect to Prophet Muhammed.

It is customery for muslims to use swt and sas respectively for Allah(swt) and Muhammed(sas).

So by speaking these two sentence with sincerety in front of a muslim a person becomes muslim, shahada means to testify, so basically a person is testifying that he/she believes that there is only one God and Muhammed is His messenger.
basically we are testifying to the oneness of God, The God of Abraham, Moses, david, Jesus and all other prophets know and unknown.

As to having doubt about certain things, as brother Jim said it is human nature to doubt and question everything, Allah(swt) says in the Quran to question, challenge, inspect and satisfy yourself about every thing. Do not follow anything or any advice blindly, Allah(swt) encourages us to use our intellect, be inqusitive.

The only way to remove doubts is to study and ask questions to knowledgeable scholars, and there are many available.
Reading Quran by ourselves is great, but to really undersatnd it we have to either have a teacher or read different tafsirs, and we need to read atleast a couple of tafsirs to actually get the gist of it.

One more aspect of being muslim is practicing moderation, Prophet(sas) said the best is to follow the middle path. that is avoid either exterme. In essence as Allah(swt) says in Quran, we have made this deen(religion) easy for you.

So once a person says his/her shahada, He/she is a muslim. but there are certain obligations on him/her to become a practicing muslim.

1. obligatry prayers 5 times a day
2. Zakat
3. Fasting during Ramadan
4. Hajj

Islam defines anything which is harmful to you, your family, your community, humanity at large and all living things to be sin, as a muslim we are commanded to stay away from sins.

Read more and post discussion or debate:  Beyond Shahada