Future Tense in Spanish

Regular

Infinitive + ending

firmaré
firmarás
firmará
firmaremos
firmaréis
firmarán

Regardless of whether it's an ar/ir/er verb, the endings will always be the same. It's just important to look out for the irregulars.

Irregular

There are many irregular future/conditional words in Spanish, and they are the same in both tenses.

Add a D

A small number of Spanish verbs use a modified version of the infinitive for the future. There, they usually add a d.

Poner pondré
Tener→ tendré
Venir→ vendré
Salir→ saldré
valer→ valdré

Drop the E

caber→cabré
haber→habré
poder→podré

querer→querré 
saber→sabré

Shorten infinitive

decir→diré
hacer→haré

Take out accent

oír → oiré
reír→reiré
sonreír→sonreiré

Compounds of irregulars

If the stem of the word is irregular, the compound word will be too. For example poner is irregular, so componer will behave in the same way. This works for all words with irregular stems.

Uses

In addition to it being used as referring to the future, it can also be used as "probably". For example, you can say "Serán las ocho." which would mean "It's probably eight o'clock."

Conditional Tense in Spanish

Here, the conjugation is essentially the same as the future. The rules are the same, and the ending is the only thing that changes.

firmaría
firmarías
firmaría
firmaríamos
firmaríais
firmarían

Irregular

The irregulars are exactly the same, which makes the conditional a lot easier.

Uses

The use of the conditional tense is mainly used as the world "would". 

Me gustaría tener un coche caro. (I would like to have an expensive car)
Juan dijo que iría. (Juan said he would go)

This is also used with si + imperfect subjunctive

Si pudiera, haría, pero no puedo, así que no haré. (If I could, I would, but I can't, so I won't.)

This is also used as the word "probably" sometimes (LESS OFTEN THAN FUTURE).

El niño tendría nueve años. (The kid was probably nine years old).