Being new to cryptography is one thing, but you are supposed to do some research on your own before asking questions here (see How to Ask), and D.W. gave you the right directions already.

But since you wanted names and links:

• The first stop should be discrete logarithm on Wikipedia, and it lists several algorithms on this topic.
• As a beginner, start with Babystep-Giantstep and Pohlig-Hellman.
• Your next stop should be Index Calculus.
• Additionally, there are algorithms based on the NFS, e.g. described in Gordon's paper Discrete Logarithms in GF(p) Using the Number Field Sieve. Current records modulo primes employ this technique.

Being new to cryptography is one thing, but you are supposed to do some research on your own before asking questions here (see How to Ask), and D.W. gave you the right directions already.

But since you wanted names and links:

• The first stop should be discrete logarithm on Wikipedia, and it lists several algorithms on this topic.
• As a beginner, start with Babystep-Giantstep and Pohlig-Hellman.
• Your next stop should be Index Calculus.
• Additionally, there are algorithms based on the NFS, e.g. described in Gordon's paper Discrete Logarithms in GF(p) Using the Number Field Sieve. Current records modulo primes employ this technique.

Being new to cryptography is one thing, but you are supposed to do some research on your own before asking questions here (see How to Ask), and D.W. gave you the right directions already.

But since you wanted names and links:

• The first stop should be discrete logarithm on Wikipedia, and it lists several algorithms on this topic.
• As a beginner, start with Babystep-Giantstep and Pohlig-Hellman.
• Your next stop should be Index Calculus.
• The most efficient algorithm right now (and most complex) is the GNFS, but don't bother with it unless you understood the others.

Being new to cryptography is one thing, but you are supposed to do some research on your own before asking questions here (see How to Ask), and D.W. gave you the right directions already.

But since you wanted names and links:

• The first stop should be discrete logarithm on Wikipedia, and it lists several algorithms on this topic.
• As a beginner, start with Babystep-Giantstep and Pohlig-Hellman.
• Your next stop should be Index Calculus.
• Additionally, there are algorithms based on the NFS, e.g. described in Gordon's paper Discrete Logarithms in GF(p) Using the Number Field Sieve. Current records modulo primes employ this technique.