In order to speak Spanish more fluidly you should be able to employ some key expressions that will help you connect your ideas. Some common phrases that are used to express a contrast between one idea and another include:

• Sin Embargo
• No obstante
• A pesar de (que)
• De todos modos
• Aunque

Although there usually isn't a single word-for-word translation of these terms, they do tend to correspond to specific words in English.

sin embargo - used like "however," or "nevertheless."

• Normalmente me gusta la cerveza, sin embargo esta marca no me agrada.
  I normally like beer; however, I don't care for this brand.

no obstante - often corresponds to "in spite of," or "nevertheless."

• No obstante el calor, pasamos mucho tiempo afuera.
  In spite of the heat, we spend a lot of time outside.

a pesar de - is often used like "despite."

• En fin ganamos a pesar de la buena competencia.
  In the end we won despite the good competition.

de todos modos - is often equivalent to "anyway."

• Estaba lloviendo pero anduvimos en bici de todos modos.
  It was raining but we went biking anyway.

aunque - can be used like "even if," or "even though" depending on the level of probability that the action will occur.

• Aunque está tu hermano no nos ayuda.
  Even though your brother is there he won't help us.
• Aunque esté tu hermano no nos ayuda.
  Even if your brother is there (which I don't think is the case) he won't help us.
• Aunque estuviera tu hermano no nos ayudaría.
  Even if your brother were there (which is not the case) he wouldn't help us.

There is also a group of useful terms for ideas that do not contrast, but rather support one another. For example:

• Así que
• Por lo tanto
• Por eso

así que - is commonly used like "so" or "thus."

• La película empieza a las siete, así que tenemos que llegar un poco antes.
  The movie starts at seven so we have to get there a little before.

por lo tanto - generally corresponds to "therefore" and is somewhat formal in tone.

• Los resultados concuerdan con la hipótesis; por lo tanto, se puede decir que el tiempo de reacción es influido por la visibilidad.
  The results agree with the hypothesis. Therefore, it can be said that reaction time is influenced by visibility.

por eso - is a common term in spoken language that has many uses and equivalents like, "due to that," "because of this," or "that's why."

• Juan es muy bajo y por eso nunca ha jugado bien el básquetbol.
  Juan is very short and that's why he has never played basketball well.