The most important thing to remember about proper finger notations is that the THUMB is notated as "T" and not by the number "1". The other four fingers are designated "1--2--3--4".
The strings are NUMBERED in Reverse Order. Start from the string on the bottom and number from 1 to 6. The heaviest or Bass (lowest sounding) string is the 6th string. It is the TOP string on the guitar. The lightest (or highest sounding) string is the 1st string. It is the BOTTOM string on the guitar. This appears a bit backwards at first, but not for long.
ALSO-- learn the strings randomly, as well as in order. If I were to ask you, "what is the 4th string?" you should be able to immediately answer, "the D string". Conversely, if I asked you, "which string is the B string?" you should be able to tell me, "the 2nd string."
There are a number of memory tricks or techniques for remembering the string names. You may NOT think of this-- learning the strings-- as important, but you will soon see its importance. Use the following acrostic sentences (if helpful) as memory tools.
E-very A-ngry D-og G-rowls and B-arks at E-veryone
E-ddie A-te D-ynamite. G-ood B-ye E-ddie.