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Basic Rules
In Stud Hi-Lo each player gets dealt an individual hand. That hand comprises of 2 cards down and 1 card up to start, and 3 cards down and 4 cards up by the end. The betting happens on each street from 3rd to 7th inclusive. The best 5 card poker hand wins half the pot, and the best low hand (using cards A to 8) wins the other half of the pot.
Starting Hands
The best starting hand in Stud Hi-Lo is AAA, followed by 888 down to 222, followed by KKK down to 999. Naturally getting trips as a starting hand is rare (0.23%), therefore dont sit around waiting for them.
3 lows to a flush are good, particularly if it includes an ace. eg Ah 2h 3h is a strong hand and very simple to play; it is the strongest un-made hand in Stud Hi-Lo.
3 connected lows are good, eg 3 4 5. The more the gaps the weaker your hand will become.
Pairs of Aces, Kings, and Queens are good.
Now Stud Hi-Lo is a fantastic game of skill, one of the highest skill factors of any poker game, so dont feel the need necessarily to be regimented just to these sort of starting hands, as others can be strong once upcards and hand-to-hand comparisons are factored in.
Strategy
4th street is very key in Stud Hi-Lo. 4th street is the last street where the cost of 1 bet is only half of 1 big bet. From 5th Street onwards, the cost of 1 bet will be one whole big bet. ie all streets after 4th are twice as expensive. Also at 4th you have generally seen a very high percentage of the dead cards that you are likely to get to see in the hand. Also at 4th you generally have the first proper indication of the type of hand that your opponents are probably playing for.
Tracking cards is very imporant in Stud Hi-Lo. It will dramtically alter your chances of hitting your hand or analysing your comparitive hand correctly. Simple examples include:
i) tracking the number of dead spades, when you are starting with a 3-spade starting hand.
ii) tracking dead low-outs. In a common sort of scenario, you may have 4 lows by 4th street, and are therefore drawing to 16 potential cards with a 71% chance of making a low by 7th. Now if 8 of those 16 are played out as dead (eg door cards or 4th street cards of opponents) then your chances of making it are reduced dramatically down to 50%.
iii) tracking 4s and 5s for dead low straights
A bit more on tracking 4's and 5's specifically. Every low straight must contain a 4 and a 5. Therefore tracking these is very important. If either the 4s or the 5s are all dead then you cant make a low straight, and conversely, if either the 4s or the 5s are dead to your opponent, they cant make one. (eg 3x4's gone in dead-cards, and you have 1x4 in your hand)
It is better to scoop just one heads-up showdown pot, than to go seeking numerous that you will only likely split down the middle. There is very little to be gained by constantly going after pots where you can only win not much more than half the antes and the bring-ins. The gains (compared to risk) are miniscule compared to the average pot that goes to showdown and scoops. Playing a hand down weakly, to then end up scooping by a distance, is also just as bad. You really need to build pots where you have a good chance of scooping (or of taking a 2:1 or 3:1 cut) by betting and raising those; and to avoid regularly chasing down hands looking for one half (eg low only vs showing high, heads-up).
Following on closely from that, remember that there will always be a high hand, but there wont always be a low hand. A common mistake that players make is to play for the low as long as they just happen to have a bunch of low cards. Always try to keep a good high in mind, and if the cards to that straight or flush start to dead out then remember you need to have the brakes majorly on and only indeed continue at all if the comparitive carding is working in your favor.
Compartive cards - it is naturally important to compare the relative value of your hand against your opponents upcards and potential hand. Commonly this is most often done with comparing lows as the information is better. Say with villain showing 278, and you on A4856 you naturally should be getting more bets in.
Probably one of the most important of all strategy elements in Stud Hi-Lo is hand direction comparisons. If 2 or more players look as though they are playing for the low, then you should really be pushing your high hand even if it doesnt seem that strong. Conversely if 2 or 3 players seem to be battling it out for a high, you with the low or a good low draw, need to be really pushing the betting. Dont go along as a passenger with a vacant smile on your face when you win a mid-sized pot at the end. Every single bet counts, and you must push these scenarios hard. If you lose the odd one so what, it doesnt matter in the bigger scheme of things. The ones you win you want to win big so play hard when the hand directions are imbalanced in your favor. In particurlar on the high side, with raindow up, and with dead 4s or dead 5s, and 2+ low showing/betting opponents, you need to push that like crazy, even if you only started with a high pair and you are yet to even hit 2 pair. Dont be passive. Many villains will brick out and fold at 7th, many will take it all the way and lose the battle of the lows, but none of that is your concern, you just want to milk them for every ounce out there at 2:1.
Due to the shear importance of card-tracking and comparitive carding to gain a consistant edge in Stud Hi-Lo, multi-tabling too much Stud Hi-Lo at once is never a good idea. Start with 1 or 2 tables until you are rountinely making quick and correct decisions about when to push the betting and when to limit the betting/fold. Take time to go over many of your hands after the fact to cement the fact that the aggressive pots were at the right times, and that passivity does not exist in times when the conditions were right to push it.
Tools to help with card tracking
You may wish to consider Stud Inspector ($99).
Also on certain poker sites you can set the chat box comments to include all info, and then detach the chat box, you will then see all dead-cards listed even though they are no longer visible at the table.