Pathfinder Unchained introduces a lot of new material in the form of alternate rules that may be used in any campaign. As it's entirely optional, and some of it is intentionally contradictory, it is necessary to clarify what is available from the book to be used. Material from Unchained comes in three forms: new rules which are mandatory and apply to every character; new options that are available to any character should they choose to invest in them; and new classes that supersede the old ones.
Fractional Base Bonuses: This causes you to add your total class levels together to determine BAB and save bonuses. Only relevant for multiclassing.
Background Skills: This system gives every character new skill points that may be spent in certain background skills to add more flavor to their character.
Alternate Crafting and Alternate Profession Rules: This simplifies and for the most part improves the mundane crafting and profession systems.
Skill Unlocks: These are bonuses you get for every 5 ranks in a skill, this mostly applies to the Unchained Rogue, but anyone can access them with a feat. Don't use the skill unlocks on the SRD, use the one linked here.
Variant Multiclassing: This system allows a character to give up five feats over the course of their career to gain certain class features from another class. This does not replace regular multiclassing.
Scaling Items: These special items grant a variety of interesting bonuses and are designed to scale in power as you level up. Instead of costing a percentage of wealth by level, you can purchase them at any level you can afford, and increase them to the next level value or higher by sacrificing components equal to the difference in value in an 8 hour ritual (no crafting feats required). See here for additional information.
Combat Stamina: This system is allowed via the "feat access" option, meaning you gain a stamina pool when you take the Combat Stamina feat, and can spend it on that feat or any other applicable combat feat (most combat feats have a stamina option).
The Monk, Summoner, and Rogue from Unchained are pretty well balanced tier 3 classes (though see the adjustments page) and are available to play. These versions supercede the old ones, which no longer exist for any purpose. Class features from other classes that reference these, such as an Investigator gaining a Rogue Talent, now use the Unchained version as well.
The Unchained Barbarian is not going to be used, but if you're playing a Bloodrager and would prefer to select a Rage Power from the Unchained Barbarian you may do so in place of the normal version (either option remains available).
For the Summoner and Rogue, they may use any option printed in other books (such as evolutions or talents) and the Unchained versions of these only supersede the existing ones. They may also use any archetype they qualify for as normal, modifying the Unchained version of the class.
The Monk may use some archetypes, but because their class features were significantly changed these will have to be addressed on a case by case basis.