Lets see, I'll start with the difference between this system and 3.5/pathfinder and work towards advice as I go:
-Rather than putting points in skills as you level up, you either have the skill or you don't, but the only difference between trained and untrained is your proficiency bonus. Remember, your proficiency bonus scales with CHARACTER level, not class level. Every class has 2 saves they are proficient in, multiclassing does NOT grant additional proficiencies. There are now six saves, each being one of your starting attributes.
-MOST buffs and debuffs now develop in the form of advantage or disadvantage now, so get a good understanding as to how that works. Otherwise bardic inspiration and Battlemaster superiority dice can alter situations by up to 1d8 (greater for higher level fighters) depending on the circumstances. A couple of spells (guidance cantrip and bless) will add 1d4 whereas bane will subtract from certain roles, but for the most part, it's all dealt with in advantage/disadvantage. Example: One of the best features of a barbarian is reckless attack. Declare recklessness, attack with advantage (roll two and pick the highest), but leave yourself open to attacks from your enemies (they get advantage vs. you). Aside from increasing chance for success, you double the chance of rolling a natural 20.
-Spell slots work differently in this edition and an 'average' between different casting classes is calculated with lesser casters obviously counting for less. Warlocks are the exception, their spell slots remain on a seperate table, but recharge/short rest BUT can still be used for non-warlock spells. Also, wizards now memorise their spells much like clerics and druids now. You can memorise X/day and can cast the same one repeatedly so long as you have the spell slots to spare.
-Be mindful that just like in prior editions, there are multiclass attribute requirements in 5e. Otherwise, you don't have to worry with a pure build and can rig up your stats as unconventionally as you like.
-Remember that RAW, your backgrounds are customisable, the jist of it being that skills can be swapped for other skills and tools and languages are interchangeable, but follow the guidelines for further info. This is quite a fun part of character creation as it provides a good template to quickly and conveniently set out your story in summary. Example: You may take the outlander background for example and re-skin it as 'skald', changing Athletics for performance and maybe swapping your bonus language for an additional musical instrument proficiency. Don't forget that each background has a 'Feature' which is almost like a very minor feat, but normally one that adds flavour to your character. For example, the Charlatan's False ID Feature is often very interesting with some characters.
-Make sure not to focus too much on optimisation. I have found it can be easy to do in this edition compared to others, probably because in my opinion, many of a subclasses more exciting powers are given to you at lv3 and lv6, but don't get bogged down thinking about that stuff, because you end up with a character that is very boring. Less a character and more just a composite of min/maxed classes. Try and work out your concept, a rough picture in your head as to what your character would be like etc and go from there, work out your primary stats and go for it.
-Take a look at some of the rules in the PHB combat section for the way grappling, shoving etc works now. These can be fun occassional tactics to use on enemies.
-Feats are more powerful in this edition than in others and some are REALLY fun. The Actor feat is one such feat that adds loads of flavour to a character. For combat, my favourite for fun would have to be shield mastery. It can be quite satisfying utilising shield bashes as a variant human fighter at early levels, rewarding too!
-Rather than putting points in skills as you level up, you either have the skill or you don't, but the only difference between trained and untrained is your proficiency bonus. Remember, your proficiency bonus scales with CHARACTER level, not class level. Every class has 2 saves they are proficient in, multiclassing does NOT grant additional proficiencies. There are now six saves, each being one of your starting attributes.
-MOST buffs and debuffs now develop in the form of advantage or disadvantage now, so get a good understanding as to how that works. Otherwise bardic inspiration and Battlemaster superiority dice can alter situations by up to 1d8 (greater for higher level fighters) depending on the circumstances. A couple of spells (guidance cantrip and bless) will add 1d4 whereas bane will subtract from certain roles, but for the most part, it's all dealt with in advantage/disadvantage. Example: One of the best features of a barbarian is reckless attack. Declare recklessness, attack with advantage (roll two and pick the highest), but leave yourself open to attacks from your enemies (they get advantage vs. you). Aside from increasing chance for success, you double the chance of rolling a natural 20.
-Spell slots work differently in this edition and an 'average' between different casting classes is calculated with lesser casters obviously counting for less. Warlocks are the exception, their spell slots remain on a seperate table, but recharge/short rest BUT can still be used for non-warlock spells. Also, wizards now memorise their spells much like clerics and druids now. You can memorise X/day and can cast the same one repeatedly so long as you have the spell slots to spare.
-Be mindful that just like in prior editions, there are multiclass attribute requirements in 5e. Otherwise, you don't have to worry with a pure build and can rig up your stats as unconventionally as you like.
-Remember that RAW, your backgrounds are customisable, the jist of it being that skills can be swapped for other skills and tools and languages are interchangeable, but follow the guidelines for further info. This is quite a fun part of character creation as it provides a good template to quickly and conveniently set out your story in summary. Example: You may take the outlander background for example and re-skin it as 'skald', changing Athletics for performance and maybe swapping your bonus language for an additional musical instrument proficiency. Don't forget that each background has a 'Feature' which is almost like a very minor feat, but normally one that adds flavour to your character. For example, the Charlatan's False ID Feature is often very interesting with some characters.
-Make sure not to focus too much on optimisation. I have found it can be easy to do in this edition compared to others, probably because in my opinion, many of a subclasses more exciting powers are given to you at lv3 and lv6, but don't get bogged down thinking about that stuff, because you end up with a character that is very boring. Less a character and more just a composite of min/maxed classes. Try and work out your concept, a rough picture in your head as to what your character would be like etc and go from there, work out your primary stats and go for it.
-Take a look at some of the rules in the PHB combat section for the way grappling, shoving etc works now. These can be fun occassional tactics to use on enemies.
-Feats are more powerful in this edition than in others and some are REALLY fun. The Actor feat is one such feat that adds loads of flavour to a character. For combat, my favourite for fun would have to be shield mastery. It can be quite satisfying utilising shield bashes as a variant human fighter at early levels, rewarding too!