I know seguir means 'to follow', 'to continue'. However I've seen it many times being used to mean 'still' or at least translating to 'still'.
For example:
Mi hijo sigue en Londres por el trabajo My son is still in London for work
Sigue lloviendo It is still raining
What is the proper way/grammer to use it while using seguir to mean 'still'?
It seems like you know the literal meaning of "seguir", which in the case of your question would be "to continue". While I'm not a big fan of literal translations, if you translate these sentences it still makes sense:
Mi hijo sigue en Londres
Would be:
My son continues in London
You just need to accept the fact that different languages use different constructions in their sentences.
By the way, you can also say:
Mi hijo aún/todavía está en Londres
The only difference would be that this sounds like there's a certain stress on the fact that it's been a pretty long time and you're awaiting his return, but this is very subtle and doesn't need to apply at all times.
As to how to construct sentences in this manner, I think it'l be best for you to check up all the meanings of the verb "seguir", you'll notice there are quite a few:
seguir
Del lat. vulg. *sequīre, y este del lat. sequi 'seguir', con la t. de ire 'ir'.
1. tr. Ir después o detrás de alguien. U. t. c. intr.
2. tr. Ir en busca de alguien o algo; dirigirse, caminar hacia él o ello.
3. tr. Proseguir o continuar en lo empezado.
4. tr. Ir en compañía de alguien. Vine con él y le seguí siempre.
5. tr. Profesar o ejercer una ciencia, arte o estado.
6. tr. Dirigir la vista hacia un objeto que se mueve y mantener la visión de él.
7. tr. Observar atentamente el curso de un negocio o los movimientos de alguien o algo.
8. tr. Tratar o manejar un negocio o pleito, haciendo las diligencias conducentes para su logro.
9. tr. Conformarse, convenir, ser del dictamen o parcialidad de alguien.
10. tr. Perseguir, acosar o molestar a alguien; ir en su busca o alcance. Seguir una fiera.
11. tr. Imitar o hacer algo por el ejemplo que alguien ha dado de ello.
12. tr. Dirigir algo por camino o método adecuado, sin apartarse del intento.
13. prnl. Dicho de una cosa: Inferirse o ser consecuencia de otra.
14. prnl. Dicho de una cosa: Suceder a otra por orden, turno o número, o ser continuación de ella.
15. prnl. Dicho de una cosa: Originarse o causarse de otra.
Our specific use case would be number 3:
- tr. Proseguir o continuar en lo empezado.
Usually one would use [seguir] + [gerundio] like "Sigue estudiando" or "sigo buscando", but our case is a bit specific and special, when we say something "sigue estando aquí", we don't need the "estar" verb in the sentence, so we end up with just "sigue aquí".
sigues siendo bonita could be rephrased as sigues bonita?
The easiest way to see it for an English speaker is recalling the verb to keep. In general, we can say that
Seguir + ando/endo = Keep + ing.
So
Sigue lloviendo = it keeps raining.
Check that it is exactly the same structure (verb+ing). It's not weird.
Of course, this can be reworded as It is still raining, and many others.
My son continues in London for work.It continues raining.just think of it as in Spanish, to continue [doing] something is a way of expressing something is still happening.