As someone suggested a small startup-guide, I try to do one from my personal point of view...
Preamble
Prior doing anything other: do the training and take a close look at key-bindings! Flying into stations is challenging... 
you may want to unbind/remap the key for "drop all cargo" (it's too close to often used keys). I highly recommend a joystick, btw...
Abbreviations
Some terms specific for Elite Dangerous are generally abbreviated, so it's nice to have an overview:
- CZ - Combat Zone (may be H-CZ or L-CZ for Hight intensity and Low intensity)
- Cx - Class x weapon (1-4, may be CxG or CxF for gimballed or fixed)
- DBS - DiamondBack Scout
- DBE - DiamondBack Explorer
- ED - Elite Dangerous
- FA - Flight Assist
- FED - local authority
- FSD - FrameShift Drive
- KWS - Kill Warrant Scanner_
- RES - Resource Extraction Site (may be H-RES or L-RES for Hight intensity and Low intensity)
- USS - Unidentified Signal Source
- SC - SuperCruise
- SCB - Shield Cell Bank
Which missions?
The starting Sidewinder is a nearly useless ship, so forget normal trading/mining/bounty-hunting immediately. You want missions from bulletin board - but pick carefully: Learn the meaning of icons. (Commander Forlon did a great overview: Bulletin board (with icons) ). Avoid missions where cargo is sought and you have to find it (at some stations or by shooting some other ships or by cruising to "unidentified signal sources"), as the sidewinder is just not fitted for such things (stations require some searching and by chance systems are not reachable. Searching loot includes dropping at USS where can be pirates. Shooting other ships - good luck in Sidewinder). Do hauling jobs where they give you the cargo and you have to ship it somewhere or smuggling-jobs (same as before, the ones where they give you the cargo).
Note that you can accept more than one mission at a time.
Finding a way
Prior accepting a mission, check if you can reach the system they want you to go! There are two ways how to do that:
- From Cockpit: hit "1" (for left panel) and go into the "navigation" tab (by pressing "q/e"). With "w/s/a/d" you can navigate within a tab. At navigation tab, you can scroll down the list of possible targets within your current jump-range (sorted by distance) until the system you want to travel comes up. Hit "space" two times to lock it into your flight-computer. Done. Later, when reached your target system, you have to bring up navigation-tab again and select the station you are heading to as new target.
Beware that the current jump-range is not the same as when cargo is full!
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From Maps: same as before, but in navigation tab, select "galaxy map" and search your destination. There is a slider-bar at bottom-left, allowing you to see your jump-range when laden. Now select the system and plot a route directly (via icon) or open system map for your target system and choose station directly as target and plot route.
First SuperCruise/Jump
After leaving station, you find a compass left side of your radar containing a dot/circle. Circle=target behind, dot=target in front. Fly away from station until "mass lock" is disengaged, then hit "j" and point ship direction of target. If target is in same system, you go to SC (super-cruise) and have to slow down when reaching target, pressing "j" again to drop out of SC near station. If target is in another system, you'll jump to the biggest mass in that system (sun) and come out in SC. Select your target station and fly there, slow down in time and drop out of SC. From 7.5km afar, you can get landing clearance (important!) by the left panel --> contacts --> station --> request docking. fit through the slot, find your place and don't forget landing-gear. Go to bulletin board and finish your mission.
What to do if smuggling?
Basically the same as with standard-trade, but you must avoid getting scanned (it's a big negative impact on reputation). Outposts very seldom (never?) scan you, but bigger station tend to do it near the station and when passing the gate. Here comes SPEED and partly "silent running" into play. Silent running shuts your heat emission, allowing you to become nearly invisible on radar, but you still can be scanned. To ensure that you will not get scanned, is needed to be fast (practice is needed).
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Starting: raise landing-gear and hit silent-running well before flying through the slot. Keep heading away from station and let temps raise until 90-95%, then normal running, wait to cool down a bit and jump away.
Landing: Stay 8-10 km from station until you see the entrance (directly to entrance is better), start your run (fast) ... At 7,5km ask permission from base, engage silent-running and go inside. Once you're inside (few meters away from mail-slot) you can disengage silent running again AND duck above or below entrance (to break line of sight patrolling ships outside which will cancel possible scans).
- Latest details for smuggling included hints & tips & guides (ED: Horizons) are here: Smuggling tips (Horizons)
But I want to fight!
For the hotter tempered, there is a way to make credits_ when fighting even in the Sidewinder:
- install a KWS (optional) to increase you income (you have to assign it to a weapon-group and do the scan by hand. It shows, if target has bounty in other systems.
Note: If you scan a "clean" target and bounties of other systems show up and you attack it, you will commit a crime in the current system and be hunted by FEDs.
- find a RES (they are located in rings of planets or asteroids) and drop out of SC there. there should be wanted targets showing up regularly. Scan them with KWS and wait for the FEDs to attack them. Or fly where you see laser-fire and look who the FEDs are shooting at. You need to land the last shot on target in order to get the bounty. A well timed shot can let your Sidewinder kill an Anaconda!
- Same can be made at USS, as sometimes pirates are there, too...
- Make sure your cargo is empty - else the pirates may choose you as target!
Doing smuggling, I made 800k in nearly no time and got myself a Cobra, which already is a beautiful ship which can be fitted for nearly all purposes. Equipment always has the same value, so you don't loose credits when switching it. However, not every equip is sold anywhere. But that allows to totally respec your ship for different purposes. If you trade a ship in order to get a new one, you'll get 90% of ship and internal costs.
Turn rate and being interrupted
Ship has best turn rate in the blue area of speedometer. So when you navigate (e.g. into a station) try to stay in that range. If someone tries to interrupt you in SC, set thruster_ into the blue range and try to stay with the escape-vector. NPCs are usually relatively easy to evade. If they manage to drop you out of SC and you don't want to fight, set power to engines (max) and shield (rest) and boost out of range of guns without turning much. Keep running until FSD is up again and disappear in SC.
What ship comes next?
just want to point to 3 ships which I find resonable, but that is of course personal:
- Explorer: Hauler. It has a stunning jumprange for such a cheap ship.
- Allrounder: Cobra_Mk III. Has range, has cargo, can fight, many internal slots, only two utility slots.
- Fighter/Smuggler: DBS. Has agility, has small profile when facing enemy, runs cold, lacks internal slots, four utility slots
Cheaper Cobra_mk3 setup
Below is shown cheaper variant for Cobra_Mk3 which can be used for haul cargo or do some PvE combat. Please be sure that you have enough spare money for few rebuys after you finish with ship equipping, this is GENERAL advice to all cmdrs! Flying without "rebuy" is assured way to basic ED ship (Sidewinder). You can use below shown ship-builder for doing changes like you wish.
... hope that helps a bit to whom may be concerned... 
Edit: Updated 20/09/15
very versatile multipurpose with much more choices in fitting than Startwinder (and one of the fastest ships in game, out-running nearly everyone else and out-gunning the one(s) who can follow). As example how equipping a ship works in terms of prices... the 
As comparison: An "okay" trade-run (no mission) in standard Sidewinder (with 4t cargo) gives you around 4k creds. Snuggling gave me missions between 20-120k creds...
... is awesome when you can take more as only one mission at once 
